Today, I had an interesting online debate with a couple of peers of mine from grad school. As you may know, I'm an avid rock climber and have a graduate degree in environmental studies with a focus in environmental education. So while out for a run, I discovered a large glacial erratic big enough to climb on and posted an iPhone photo of the boulder on my personal Facebook page. In the caption, I mentioned that the boulder needed some cleaning, a term climbers use to describe removing debris and sometimes mosses and lichens from the surface of a rock to make it suitable for climbing. What ensued was a lengthy debate of the ethics of rock climbing and bouldering, where two of my grad school classmates (both environmental studies students with a concentration in conservation biology) argued that cleaning a boulder to climb on was selfish and destructive and that climbing in general was an activity detrimental to the environment. We went back and forth a bit, respectfully, and it's possible that some feelings got hurt. The reason I bring this up is because in our discussion I noticed something very interesting. While my classmates were so quick to critique my mention of cleaning a boulder, they've never criticized, critiqued, or even questioned my other actions that take place in nature, and in the whole scheme of things, cleaning a single, easy to find boulder not far from a well used (and heavily impacted) pathway is really low on the scale of things I do with potentially destructive environmental impacts.
For years, my main source of income came from nature photography. To make that work, I spent countless hours in the field, interacting very closely, often intimately, with wildlife and natural landscapes. Yet rarely does anyone ever question the impact of me doing so. People don't ask me if I trampled native plants or disturbed an animal to get a shot. They just ooooh and ahhh at the aesthetically pleasing results of my work and only rarely question the methods I use.
I know the general public is unaware of what goes into a nature photograph and potentially how much manipulation, impact, and destruction are a part of the photographic process. Issues like moving branches or rocks, using calls and sounds to mimic other animals in distress, stalking feeding or nesting areas, and attracting wildlife with bait probably don't occur to most people. But most people probably think little of the impact rock climbers have either, so why should two educated, environmentally minded people worry about my relatively isolated and infrequent climbing impacts while ignoring my photographic ones.
[If] I shared a photograph of a loon (which I will at some point soon) I doubt you'd question whether I got too close to the loon and disturbed it, or if I sanitized my boat for milfoil and other organisms that could be transported between waterways and contaminate "pure" ecosystems before plopping my kayak in the water to take that picture. No one has ever asked if I baited the owl in that beautiful snowy owl shot I have that everyone loves (for the record, no I didn't, but a lot of snowy owl photos you see are from animals that have been lured with the promise of a meal of pet shop feeder mice). You trust me enough to be a responsible and ethical nature photographer (or maybe you just never thought about it). Please trust me to be an ethical climber too.
The truth is I try to be responsible in everything I do in the outdoors. I'm not perfect, but I realize that my existence impacts the environment around me every day. When I am hands on in the environment, be it rock climbing or taking photographs, these impacts are more direct. I step on and crush plants! I startle and disturb animals! I make noise and track toxins and species from one location to another. My presence in the environment undoubtably changes it, but I do try to minimize my negative impacts as much as possible. So I look where I step and give wildlife its space when possible. I stick to well worn paths or wander off trail on surfaces that can best handle the pressure of my feet, avoiding the rare or intermittent plants in favor of rocks, bare ground, or hardier, more commonplace species. When photographing animals, I carefully watch their behavior and back off if I sense I am distressing them or making them upset. I leave a trace, but I try to leave as small of a trace as possible or otherwise ensure that the overall impact of my presence is a positive one instead of a negative one.
I am aware of my influence on others as well. As a rock climbing instructor and an important person in our local rock climbing community, I know that how I act and behave while climbing or in the outdoors sets an example for other climbers, particularly the young ones who first venture into outdoor climbing under my guidance. As a photographer who teaches photography and sells my work, I know that my actions model my values and tell others how it is acceptable to behave when photographing nature.
I feel it is important to bring awareness to this very issue. As nature photographers, we (and all outdoor enthusiasts) need to think about what we do, and how and why we are doing it. We do impact the environment, sometimes negatively, sometimes positively, usually both. We also influence each other. Do your actions reflect your beliefs and values? Are they what you hope others would do? When given the chance, are you educating and encouraging others to act responsibly and respectfully? I hope so.
As a photographer, I believe in full disclosure (of techniques, not so much of locations). For me a good rule of thumb is if I wouldn't feel comfortable telling someone how I got a particular shot, then maybe I shouldn't do it that way. In the past I've used bird calls to attract territorial birds during mating season and crossed over fences that clearly said to stay on trail. These days, I'm not so proud of those type of actions, so I avoid them and instead stick to more natural settings and following posted signs and warnings. I'm more aware of my actions now and the potential consequences of them. Occasionally, I mess up. I'm human and inherently flawed by nature, but I try to be virtuous and most importantly, I try to be honest. And I genuinely do care.
Call me old fashioned, but I still think there's value in that.
Posted in Adventure, Education, Environment, Philosophical, Photography and tagged bouldering, conservation, environment, ethics, nature photography, responsibility, rock climbing on May 22, 2015 May 22, 2015 by Kari.
Jerry Monkman and I have been logging a lot of hours of filming for The Power of Place over the past few months. We are working on a documentary about the Northern Pass transmission line project, a proposed high voltage power line that would cut through 180 miles of New Hampshire, impacting some of the state's most iconic landscapes, including the White Mountain National Forest and Appalachian Trail. So far we have interviewed more than a dozen people and visited and filmed areas all along the proposed route. The process has involved many long days, thousands of miles on each of our cars, terabytes of disk space, and hundreds of emails back and forth, but we are accumulating a ton of good material and both of us feel like this documentary is going to actually turn into something that just might catch people's attention.
Most days after filming I am too tired or too busy to blog about it (although I do tend to post iPhone photos I shoot while out in the field to my Facebook page or to Instagram and Twitter), but I feel really guilty not talking about this project more because 1) working on it has been awesome and 2) not enough people, particularly New Hampshire residents, are well informed about this important issue.
Last night, Jerry and I spent the night atop a mountain under the stars to shoot sunset, sunrise, and the night sky in between. We've done this a couple times before by now, and I'd like to say it's getting easier, but I'm not sure that it is. Even if so, it's still hard! We rarely get much sleep (believe it or not, it is COLD in August in New Hampshire on a bald mountain summit overnight), and we are always lugging a ridiculous amount of hardware up and down steep rocky trails characteristic of New Hampshire. Regardless of how tough the journey might be, it's always a pretty awesome experience, and we are getting some great footage thanks to our efforts, so it's been 100% worth it every time.
Here is a small glimpse of what we've been up to. Jerry and I are both trying not to publish too much material that might make it into the film, but I've been taking pictures with my iPhone and even turned on my GoPro yesterday to capture some "behind the scenes" footage of the documentary process. Enjoy these snapshots and be sure to check out The Power of Place page on Jerry's website to learn more about the project.
Should you worry that our documentary is going to contain imagery of similar quality to the shots above, taken with a first generation GoPro, fear not! Despite my snap happy ways I still know how to use a high resolution DSLR and capture images that more accurately reflect how awesome the state of New Hampshire is. Here are a couple sneak peaks of the beauty we experienced last night. These are straight from Lightroom, so the sharpening and fine detail aren't quite up to my usual standards in these web versions, but I can assure you the RAW files look pretty sweet!
Jerry and I are hoping to wrap up the majority of our filming within the next month as hints of autumn are already appearing in the north country and even the swamp maples are starting to turn at lower elevations and latitudes. That means there is a lot to do between now and the end of September, so I probably better get some sleep!
Posted in Environment, Photography, Uncategorized and tagged behind the scenes, documentary, filmmaking, GoPro, Jerry Monkman, Northern Pass, The Power of Place on August 24, 2013 September 18, 2013 by Kari.
It's early, very early and still quite dark. You step carefully and slowly as your weary eyes struggle to adjust to the dim light until you finally manage to find the spot you are looking for. You set up your tripod and camera, find the perfect composition, and adjust your settings, making sure you are ready for the light show that is sure to come. Then you wait for the sun to rise.
The morning is calm, the air still save for a gentle breeze that brings the sweet scent of the nearby ocean to your nostrils. You hear the song of gulls crying out through the darkness, over the soothing woosh of the waves, as you lick the salt from your lips. Already, you can feel the stickiness of the air. All of these sensations combined touch something in your spirit. Despite the darkness and how tired you are, there is no place else you'd rather be.
And then the peace is broken. From behind you, you hear something, and it is not the call of the gulls or the woosh of the waves or even the pad-footed trot of a murderous feral cat. Instead it is the unwelcome sound of another human being.
From here the story can go a number of ways. Despite the trepidation you initially feel in your heart, the newcomer might be just a passerby, or possibly another photographer that stays well out of your way. If you are lucky, which you probably are on most days, the arrival of another person won't interfere much with your sunrise shoot. But if you aren't, which happens to most of us at one point or another, your pleasant morning can completely ruined by the intruder.
I have been both the first person at a spot and a latecomer, but I have yet to have had a negative interaction with another photographer in the field. I have heard many sorry stories however. From photographers maliciously bumping one another's tripods to tour groups crowding single photographers out of tight spots and shouting matches between workshop leaders, the type of behavior shown by some photographers in the field is downright appalling. Childish tantrums and bullying have no place in nature. I don't care whether you are the Kanye West of nature photographers or not, don't be a jerk.
Nature is a sacred place. I'm not religious, but the closest I have ever gotten to feeling a spiritual connection to anything has been when I am out in nature. Screaming hissyfits destroy the sanctity of these most serene and peaceful places.
Just a few weeks ago, I was at Sparks Lane, a very popular photo spot in the Great Smoky Mountains National Park. The sun had not yet risen and at least a dozen or so photographers were standing shoulder to shoulder on the narrow dirt road, composing the same shot of trees forming a canopy over the path, waiting for the light to get good. Everything was pretty much fine until a couple with a dog in a beat up rusted out sedan wanted to get through. The photographers parted ways to let the car down the road and then resumed position, only for the car to stop just a short way down the road in a spot that was quite plainly obviously ruining everything! The passengers, oblivious or uncaring to anything other than their own desires, just stayed there, and a few of the photographers in the group started to whistle and yell at them to move. Because I can't stand hooping and hollering on a peaceful spring morning, I walked down the road towards the car to quietly explain to the passengers that they were in our way, but they drove off right as I reached them. Just a short while later, they came back in the opposite direction and again parked in the road. This time, I got all the way up to the car and very kindly explained the situation to them: photographers had been waiting all morning for this shot – it was a beautiful morning, wasn't it? – and the light was getting gorgeous. They were in the way, and would they please consider moving? I even invited them to join us and see what a beautiful photograph they could get from our vantage point, and made sure to compliment them on how cute their dog was. While the couple in the car seemed to lack the graces of civilized society, they indeed moved on without a fuss and the photographers were able to get their shots. Instead of having to hear each other shouting and complaining, we listened to turkeys gobble as they strutted in the fields, the toms displaying for their ladies, over the hushed whispers of happy photographers and muted sounds of many camera shutters.
In the past, I have met and befriended photographers simply by walking up to them and introducing myself while in the field. I often go out in nature to be alone, so I hate when another photographer shows up on a day I've intended to shoot solo, because then I'm suddenly concerned about them – and whether I'll get in their way or they'll get in my way – instead of focused on creating images. The worst is when a big group shows up and it goes from being just me on the beach to me and ten strangers on the beach, all with cameras. I know how awful that feels, and the resentment and frustration that goes along with it. So I've resolved this problem by introducing myself to anyone I'm sharing space with and putting the situation out there early. I often say something along the lines of "Hey, I want to get good shots here and I know you do too, so I'll try to stay out of your way and I'd appreciate if you could do the same for me. I think we can both get the shots we want if we just communicate with each other – that way everyone can be happy." I do this whether it's just me or I'm leading a whole group. If I am leading a group, I make it clear to my group that the other photographer has every right to be there as we do, and if the other photographer got there before we did, I make sure they get the priority spot. I'd hate to be somewhere early, all set up, and then have a workshop show up and crowd me out, so I make sure that I don't do that to anyone else.
I've heard so many horror stories of photographers setting up right in the way of others, of workshop leaders bullying out other photographers so they and their clients can get the best shots, and of photographers with big egos just doing whatever the heck they please regardless of how it affects anyone or anything else. In some cases, bigger name tour operators have brought groups to areas where local photographers, workshop leaders, and guides have invested their whole careers and think that because of "who they are" they can do whatever they want wherever and whenever they want. They show no respect to the people who really truly know certain areas best, including sometimes their own ground agents. Etiquette, it would seem, has gone right out the door.
Nature is not a war zone. It is no place for battle, at least not between egos and a-holes. Let predator and prey clash, not us against ourselves. As photographers and people, I hope we can learn to respect one another and treat each other with kindness. If that is too much to ask, at least respect nature and keep the peace.
Posted in Environment, Philosophical, Photography and tagged keep the peace, nature, play nice, respect, sacred place, tours, workshops on May 8, 2013 May 8, 2013 by Kari.
There are many reasons why we need nature. Perhaps the one that draws me most often is its ability to bring me to a happy place, to free me my mind from negativity and confusion, and put a smile on my face and a lightness in my heart.
When I'm stressed or having a bad day, or just feeling terrible because life seems hard or the world seems kind of rotten, I go out in nature and the smell of the air, sound of the wind and water, and the excited little movements of birds and other lifeforms ease away the pain. Nature doesn't erase the ugliness of the rest of the world, but it helps restore my own spirit, giving me the strength to face it.
Yesterday, some vile person deployed explosives near the end of the Boston Marathon route. Those bombs killed at least three people and injured more than 140 more. Runners and spectators suffered severe injuries, some losing limbs. One of those killed was an eight year old boy.
I'm in Florida right now, many miles away from Boston. I feel helpless, as I'm sure I would even if I had been home in New Hampshire, only two hours from the city. Still, it doesn't make any sense, and down here, even with the tragedy on every television I come across, I feel isolated in my pain. When devastation hits so close to home and touches something you love and that has become a part of you, you feel it differently I think.
I was in Back Bay, the area where the explosions occurred, just one month ago visiting friends. I knew runners in the marathon – some were teammates from my college track and field team. The bombings are senseless, cruel, and devastating.
This morning, I went for a run around Vilano Beach. I like to run or do some other physical activity every morning because it gets my day off to a good start, and like nature, exercise is therapeutic. Getting outside, in the fresh air, and moving helps clear my head. On my morning run, I saw a pelican and flowers. I watched the sun rise and saw the light of the day turn from blue to gold to white. Sand sparkled on the dunes, and the sweet scent of the salty ocean air mixed with the smells of spring filled my nostrils. There is a flowering vine here called confederate jasmine that I particularly love. Gulls flew overhead, laughing, their white bellies glowing in the morning light, and grackles cackled as they plucked food scraps off the sidewalk and flew them to the tops of nearby palm trees.
The world is no better nor no more evil today than it was yesterday or the day before that. During our lifetimes, we will experience a lot of cruelty and suffer many pains. Sometimes the world will seem hopeless and horrible, but it's not. For each individual that exists with cruelty in their soul and hate in their heart, there are hundreds of thousands more who are filled with love and compassion. Despite the tragedy of yesterday, I think we need to feel hopeful knowing this. I also think we need to embrace what it is we love about the world, be it friends and family, or wild things and open spaces, and be thankful for all that we have, because it really is so so much.
If like me, you are struggling to make sense of all this or another misfortune in your life, stop. Go outside. Find nature. Spend some time with her. You'll feel better when you do. She won't give you the answers to all your questions, she won't resurrect the dead, and she won't erase the bad things that sometimes happen in this world, but she'll remind you that there are so many good things too.
Posted in Environment, Philosophical and tagged Boston Marathon, Boston Marathon bombing, nature, nature therapy, terrorist attack on April 16, 2013 April 16, 2013 by Kari.
A Common Loon (Gavia immer) with a sunfish it caught while hunting on a pond in southern New Hampshire. This adult was catching fish to feed its chick.
This week, New Hampshire State Bill 89 may make it's way to the New Hampshire state senate. SB-89 is a bill that proposes banning the use and sale of toxic lead fishing tackle weighing one ounce or less, and it's passage will help protect common loons from lead poisoning.
Lead poisoning is the leading known cause of death for loons in the state of New Hampshire. Loons typically consume toxic lead in one of two ways: they either ingest the weights thinking they are pebbles, which they consume to aid in digestion, or they get lead into their system when eating fish that have lead fishing gear attached to them or in their stomachs. Poisoned loons then die a painful, suffering death. Because loons are slow to mature, have small clutch sizes, and expend a huge amount of energy in raising and caring for their chicks, these unnatural deaths have caused decreases in the loon population and continue to threaten the survival of these beautiful birds.
I cannot think of a single reason not to vote in support of SB-89 and these increased restrictions; there are a number of viable alternatives to lead that can be used for small sinkers and jigs, and their continued use is irresponsible.
More info about loons, lead poisoning, and SB-89, including what you can do to help, can be found here: http://www.loonbill.org/getinvolved.html.
A Common Loon (Gavia immer) in its handsome black and white breeding plumage swims on the calm surface of a pond in southern New Hampshire.
The Loon Preservation Committee is a great organization that advocates for the protection of these beautiful birds in New Hampshire. I was able to connect with them last summer and they were helpful in providing me with some information about loons in NH. Unfortunately, I was unable to spend as much time working with them as I wanted, but hope to continue a project to document and advocate for loon conservation in the northeast with their help. For more info, visit http://www.loon.org/.
A baby Common Loon (Gavia immer) begs its parent for some food. This youngster is growing up and white and dark gray feathers are starting to replace its mousey gray-brown down.
Posted in Environment, Photography, Political and tagged common loon, Gavia immer, lead poisoning, loon, loon mortality, Loon Preservation Committee, New Hampshire, NH, SB-89 on March 12, 2013 March 12, 2013 by Kari.
I live in a beautiful restored farmhouse in Chesterfield, New Hampshire, just six miles or so (as the crow flies) from an aging nuclear power plant in Vernon, Vermont. Vermont Yankee, nestled on the banks of the Connecticut River, opened its doors to power production in 1972, and its 40 year contract is set to expire next month. The nuclear reactor has been the subject of much debate; everyone seems to worry about the plant's future. Many want to see it shut down, citing various environmental and health concerns and also controversial court decisions that some say pit the state against the federal government. Others worry about what will happen if the plant closes, fearing the loss of jobs and increased taxes that will result, as well as other economic and social impacts.
The Vermont Yankee nuclear power plant in Vernon, VT has inspired much debate over its 40 years of operation. Many think the plant should be shut down, but some locals worry that the impacts of shutting the plant down would be worse than its continued operation.
This weekend, I teamed up with photographers from the Vermont Center for Photography to learn a little bit more about Vernon and the people that live there. We spanned the small rural Vermont town, photographing and interviewing local farmers, business owners, town officials, and activists. Our goal was to tell the story of Vernon, not just Vermont Yankee. As we learned, there is more to the town than one nuclear power plant.
We found ourselves so inspired by what we heard, that a couple of the other photographers and I ended up working round-the-clock to piece together a multi-media presentation of our work, and more importantly, their stories. Just 27 hours after we began shooting, we presented a very rough version of at an open forum to discuss Vermont Yankee led by photojournalist Michael Forster Rothbart at the Vermont Center for Photography yesterday. Now, after roughly 36 hours of shooting, audio and photo editing, and compiling the final presentation, our piece is nearly complete; I am just waiting on final approval from my colleagues to show it to the world. Once all are happy with the final edit, which I completed at roughly 12:30AM last night, I will share the link to the video on my blog and website.
Posted in Environment, Photography, Political and tagged environmental photojournalism, Michael Forster Rothbart, nuclear power plant, nuclear reactor, photojournalism, Vermont, Vermont Center for Photography, Vermont Yankee, Vernon, Vernon Vermont on February 27, 2012 February 27, 2012 by Kari.


Stephanie Vegh is an artist and writer whose criticism has appeared in Scotland's Map Magazine, Canadian Art, C Magazine, and various British and Canadian publications as well as her own eponymous visual arts blog. She serves on the Board of Directors for The Print Studio and the Visual Arts Committee for Hamilton's annual Supercrawl, and has exhibited her drawings in group and solo exhibitions in Canada and the United Kingdom. Stephanie Vegh is the Director of the Hamilton Arts Council.


Portland's Daydream Machine began as a basement project of Jason Adams, Jonathan Allen, Matthew Strange, and Josh Kalberg, and quickly evolved with rising local star drummer/vocalist Cat Hoch. Offered up is a noir mix of West Coast neo-psychedelia, post-punk, and shoegaze a la Anton Newcombe's BJM - but with the mild and murky winters of the Pacific Northwest as our backdrop. Lose yr mind and float away, it's okay.


but its not a further crop so for dual video and still shooters the focal length doesn't change when you switch from stills to video like the EOS R does.
Cropping is for people who bought the wrong lens, sorry but cropping isn't an option for me, unless the longest lens a manufacturer makes is still not long enough then cropping is the only option.
i can vouch for panamoz, excellent service ive bought 1dx2, 5d4, 24-70, 16-35, 70-200 and 100-400 from them so far with no problems at all.
has mifsuds prices changed at all, as you are comparing 2 different shops?
Amazon, right, was that from amazon or one of their "inshop" sellers?
the 56 was £849 and is still £849, where did you see this jump?
Not if shutter speed is your primary concern it isnt. And yes it is brighter, by one stop. Period.


text:
\section{Introduction}
	The nonlinear Schr\"odinger (NLS) equation is widely used to detail water waves \cite{ac}, propagation of pulses in optical fibers \cite{at} and few other aspects in physics \cite{zhakarovv,hb,ac5}. The solutions of this equation (plane wave, solitary wave, travelling wave, breathers and RW) describe various nonlinear phenomena that occur in different areas of physics. The RW phenomenon occurs in oceanography \cite{ck}, optical fiber \cite{cl}, plasmas \cite{aa}, Bose-Einstein condensates \cite{xl}, fluid mechanics \cite{sl} and Heisenberg ferromagnet \cite{bq}. In oceanography, RWs or freak waves are the waves that appear in the open sea with very high amplitudes in comparison with ambient waves \cite{ck}. In general, tsunamis and storms can be predicted hours or even days ahead of time. However, predicting oceanic RWs is impossible due to the highly erratic nature of these waves-appearing and disappearing suddenly, without a trace \cite{na}. Physical measurements have shown that these enormous waves are capable of wrecking a ship. A complete understanding of these RWs is yet to be achieved since it is both difficult and dangerous to monitor them practically. Rogue waves appear not only in the ocean but also in optics because of the modulational instability (MI) of the background waves \cite{bkibl,na1,jms,chen4,aly}. Linear models struggle to describe the high amplitude waves that occur in the open ocean. Hence, efforts have been made to investigate these RWs using nonlinear wave theory.

	RWs arise from a variety of backgrounds such as constant \cite{km}, non-constant wave (multi-soliton and periodic) backgrounds \cite{dj,jb,wq,xg,hq,cc,wl,bx}. A literature review showed that the RW solutions have been obtained mostly through Hirota bilinearization procedure \cite{rh,yca} and Darboux transformation (DT) method \cite{yt}. Initially considerable amount of studies have been devoted to study the RWs on constant background both at theoretical and experimental level. Very recently, constructing RWs on the periodic wave backgrounds have drawn great interest in soliton theory. This is because in nature the surface of the ocean and the waves on it shows a periodic (periodic in space) or double-periodic (periodic in both space and time) pattern.

	Kedziora et al., for the first time, numerically computed periodic RWs using the DT method \cite{dj}. Chen and his collaborators developed a novel method for obtaining RW solutions on a single-periodic background for systems such as NLS \cite{chen2}, modified Korteweg–de Vries (mKdV) \cite{chen1} and derivative NLS equations \cite{chen3}. Calini and Schober were reported RWs over a double-periodic background with a more accurate numerical scheme \cite{ac1} . Based on this, recently, the method of constructing RW solutions, analytically, with a double-periodic background was presented for the NLS equation \cite{chen5}. Furthermore, Pelinovsky had computed the rate of instability for both the single- and double-periodic solutions for the NLS equation \cite{dep}. Continuous RWs were experimentally observed in laser optics and water tanks \cite{rand}. The double-periodic wave solutions are also observed experimentally in hydrodynamical experiments \cite{kim}. The analytical and numerical approaches used to study the RWs over a periodic wave background have also been extended to few other higher-order NLS equations such as Hirota \cite{wq}, fourth-order NLS \cite{hqz} and fifth-order NLS equation \cite{sinthu3}. As far as higher-order NLS equations are concerned, RW over the double-periodic wave background has been constructed only for the Hirota equation.

	The higher-order NLS equations have been frequently used to examine external elements such as sea depth, bottom friction, viscosity, and other parameters in ocean waves and ultra short pulse propagation in fiber optics. One such higher-order NLS is the fifth-order NLS equation. The fifth-order NLS equation has a wide range of applications and is of significant interest. From the optic and oceanographic study perspectives, the higher-order effects in solitons and RWs can be understood using the results of the fifth-order NLS equation. Research has focused on several aspects of constructing and analyzing the properties of localized solutions in the fifth-order NLS equation over the last two decades \cite{wzzhao,zwang, mal3,wrsun,hxjia,mwang}, including RWs solutions on constant wave background. Recently, we have studied the formation of RWs on the elliptic function background and investigated MI of the single-periodic waves for a fifth-order NLS equation \cite{sinthu3}. The fifth-order NLS equation, which we considered in our paper \cite{sinthu3}, is derived from the deformation of the inhomogeneous Heisenberg ferromagnetic system with the help of a prolongation structure. Very recently, Wang and Zhaqilao have studied RWs solutions of another fifth-order NLS equation on two different single-periodic wave backgrounds and reported how the amplitude and background waves of the RW solutions change with respect to the higher-order dispersion terms \cite{zwang}. In this present work, we aim to construct RW solutions over the double-periodic wave background and study their MI for the fifth-order NLS equation \cite{Feng,song}.

	The following explains the structure of our paper: In Section 2, we present a fifth-order NLS equation and its Lax pair and DT applicable for this equation. In Section 3, we demonstrate the underlying procedure, namley nonlinearization of Lax pair for creating background waves. In Section 4, we introduce a second solution of Lax pair equation to generate the RWs over double-periodic background waves. In Section 5, we compute the instability rate for the seed solution, which are double-periodic wave solutions of fifth-order NLS equation. The summary of our work is described in Section 6.
	\section{Darboux transformation and double-periodic solutions of Eq. (\ref{e1})}
	In the present research work, we consider a fifth-order NLS equation in the following form,
	\begin{align}
		iq_t+\frac{1}{2}q_{xx}+|q|^2q-i\delta(q_{xxxxx}+10|q|^2q_{xxx}&+20\bar{q}q_xq_{xx}+30|q|^4q_x\nonumber\\&+10(q|q_x|^2)_x)=0,
		\label{e1}
	\end{align}
	in which the function $\bar{q}=\bar{q}(x,t)$ is a complex conjugation of $q=q(x,t)$ while the function denotes wave envelope. The real parameter $\delta$ can be used independently to control the values of the fifth-order dispersion and to learn the changes that occur in the dynamics of the system (\ref{e1}).
	The variables $x$ and $t$ are placed in the subscripts of $q$ denote the partial derivative with respect to spatial and temporal coordinates, respectively.

	The existence of Lax pair (system of linear equation) for the Eq. (\ref{e1}) can be read from the following
	\begin{subequations}
		\label{s2}
		\begin{align}
			&	\varphi_{x}=L(\lambda,q) \varphi,\;\; \varphi_{t}  = M(\lambda,q) \varphi, \;\; \label{e2}\\ &L(\lambda,q)=\begin{pmatrix} \lambda & q\\ -\bar{q} & -\lambda \end{pmatrix},\;\; M(\lambda,q)=\begin{pmatrix} A_1  & A_2\\ A_3 & -A_1 \end{pmatrix},\;\;
			\label{e122}
		\end{align}
	\end{subequations}
	with
	\begin{align}
		A_1=\;&i\left(\frac{|q|^2}{2}+\lambda^2\right)+\delta(\bar{q}q_{xxx}-q\bar{q}_{xxx}+q_x\bar{q}_{xx}-\bar{q_x}q_{xx}-6|q|^2(q\bar{q}_x-\bar{q}q_x))\nonumber\\&+2\lambda\delta(\bar{q}q_{xx}+q\bar{q}_{xx}-|q_x|^2+3|q|^4)-4\lambda^2\delta(q\bar{q}_x-\bar{q}q_x)+8\lambda^3\delta|q|^2+16\lambda^5\delta,\nonumber\\
		A_2=&\;i\left(\frac{q_x}{2}+\lambda q\right)+\delta(q_{xxxx}+8|q|^2q_{xxx}+2q^2\bar{q}_{xx}+4|q_x|^2q+6\bar{q}q^2_x+6|q|^4q)\nonumber\\&+2\lambda\delta(q_{xxx}+6|q|^2q_x)+4\lambda^2\delta(q_{xx}+2|q|^2q)+8\lambda^3\delta q_x+16\lambda^4\delta q,\nonumber\\
		A_3=&\;i\left(\frac{\bar{q}_x}{2}-\lambda\bar{q}\right)-\delta(\bar{q}_{xxxx}+8|q|^2\bar{q}_{xxx}+2\bar{q}^2q_{xx}+4|q_x|^2\bar{q}+6q\bar{q}^2_x+6|q|^4\bar{q})\nonumber\\&+2\lambda\delta(\bar{q}_{xxx}+6|q|^2\bar{q}_x)-4\lambda^2\delta(\bar{q}_{xx}+2|q|^2\bar{q})+8\lambda^3\delta\bar{q}_x-16\lambda^4\delta\bar{q}.\nonumber
	\end{align}

	In the above, the function $\varphi=(\psi_1,\varphi_1)^{T}$ is the solution of the Lax pair Eq. (\ref{s2}) wherein the superscript $T$ stands for the vector transpose. The spectral parameter is denoted by the Greek alphabet $\lambda$. One can unambiguously prove that the zero curvature condition, $L_t-M_x+LM-ML=0$, commensurate to Eq. (\ref{e1}).

	The one-fold DT of Eq. (\ref{e1}) is given by \cite{mwang}
	\begin{equation}
		\hat{q}(x,t)=q(x,t)+\frac{2(\lambda_1+\bar{\lambda}_1)\varphi_1 \bar{\varphi}_2}{|\varphi_1|^2+|\varphi_2|^2},
		\label{e3}
	\end{equation}
	where $\hat{q}(x,t)$ and $q(x,t)$ are the first iterated and seed solution of Eq. (\ref{s2}). One can solve the Lax pair Eq. (\ref{s2}) with various forms of seed solutions. For example, the seed solution in the form of plane and periodic waves yield RWs over the respective background. On the other hand the choice $q(x,t)=0$ helps one to identify soliton solutions for the Eq. (\ref{e1}). Even among the periodic waves one may consider various forms to feed as seed solution. For example, one may consider the periodicity in only one direction (spatial) or in two directions (spatial and temporal) and the respective expression can be fed as a seed solution in Eq. (\ref{s2}). From a mathematical standpoint, one can observe that it becomes less tedious to solve the linear Eq. (\ref{s2}) using seed solutions that are periodic in only one direction when compared to using seed solutions that are periodic in both space and time. In the following, we solve the Lax pair Eq. (\ref{s2}) with double-periodic wave solutions (waves that are periodic in space and time) as seed solution.
	\begin{figure*}[!ht]
		\begin{center}
			\begin{subfigure}{0.4\textwidth}

				\includegraphics[width=\linewidth]{13ddpbk09a005}
				\caption{}
			\end{subfigure}
			\begin{subfigure}{0.4\textwidth}

				\includegraphics[width=\linewidth]{1cpdpbk09a005}
				\caption{}
			\end{subfigure}\\
			\begin{subfigure}{0.4\textwidth}

				\includegraphics[width=\linewidth]{23ddpbk09a005}
				\caption{}
			\end{subfigure}
			\begin{subfigure}{0.4\textwidth}

				\includegraphics[width=\linewidth]{2cpdpbk09a005}
				\caption{}
			\end{subfigure}\\
			\begin{subfigure}{0.4\textwidth}

				\includegraphics[width=\linewidth]{1cpdpbk09a01}
				\caption{}
			\end{subfigure}
			\begin{subfigure}{0.4\textwidth}

				\includegraphics[width=\linewidth]{2cpdpbk09a01}
				\caption{}
			\end{subfigure}
		\end{center}
		\vspace{-0.3cm}
		\caption{ The wave pattern profiles of double-periodic waves for $k=0.9$: (a)-(b) The phase-repeated wave patterns and its corresponding contour plot of Eq. (\ref{e4}) with the system parameter $\delta=0.05$, (c)-(d) The phase-alternated wave patterns and its corresponding contour plot of Eq. (\ref{e5}) for $\delta=0.05$, (e)-(f) are contour plots of (\ref{e4}) and (\ref{e5}) drawn for $\delta=0.1$.}
		\label{fig1}
	\end{figure*}
	To achieve our task we proceed as follows. Instead of solving the Lax pair Eq. (\ref{s2}) with doubly periodic solution as seed solution we consider two different double-periodic traveling wave solutions of Eq. (\ref{e1}), having Jacobian elliptic functions \cite{crabb}, in the form
	\begin{align}
		q(x,t)=&k\frac{\text{cn}(t,k)~\text{cn}(\sqrt{\epsilon}(x+\omega t),\tau)+i\sqrt{\epsilon}~\text{sn}(t,k)~\text{dn}(\sqrt{\epsilon}(x+\omega t),\tau)}{\sqrt{\epsilon}~\text{dn}(\sqrt{\epsilon}(x+\omega t),\tau)-\text{dn}( t,k)~\text{cn}(\sqrt{\epsilon}(x+\omega t),\tau)}e^{i t},\quad \tau=\frac{\sqrt{1-k}}{\sqrt{\epsilon}},
		\label{e4}\\
		q(x,t)=&\frac{\text{dn}(t,k)~\text{cn}(\sqrt{2}(x+\omega t),\tau)+i\sqrt{\epsilon k}~\text{sn}(t,k)}{\sqrt{\epsilon}-\sqrt{k}~\text{cn}(t,k)~\text{cn}(\sqrt{2}(x+\omega t),\tau)}e^{i k t}, \quad  \tau=\frac{\sqrt{1-k}}{\sqrt{2}},
		\label{e5}
	\end{align}
	and determine the associated eigenvalues so that they become solutions of the Lax pair Eq. (\ref{s2}). In Eqs. (\ref{e4}) and (\ref{e5}) the elliptic modulus parameter $k$ varies from $0$ to $1$, $\epsilon=1+k$ and the constant $\omega$ is related to the system parameter $\delta$ through the relation $\omega=\left(16-\displaystyle \frac{2}{k^2}\right)\delta$.

	Figure \ref{fig1} shows the unique characteristics of the double-periodic waves (\ref{e4}) and (\ref{e5}) for $k=0.9$ with two different values of system parameter ($\delta$). Figures \ref{fig1}(a)-\ref{fig1}(b) represent the three dimensional wave profile and its contour plot of Eq. (\ref{e4}) when $\delta=0.05$ respectively. Similarly for Eq. (\ref{e5}), the demonstrations are given in Figures \ref{fig1}(c) and \ref{fig1}(d). The contour plots of Eqs. (\ref{e4}) and (\ref{e5}) with $\delta=0.1$ are shown in Figures \ref{fig1}(e) and \ref{fig1}(f). Clearly, the double-periodic wave solutions (\ref{e4}) and (\ref{e5}) generate two different wave patterns, namely phase-repeated and phase-alternated wave patterns. Both the wave patterns are clearly shown in Figures \ref{fig1}(b) and \ref{fig1}(d). As the system parameter $(\delta)$ is increased from $0.05$ to $1$, the localization of waves or peaks increase in the $(x-t)$ plane when compared to lower values of $\delta(\leq0.05$). We also notice that while the system parameter ($\delta$) is varied, the orientation and the number of occurrences of a repeating wave pattern of both the waves are slightly change as illustrated in Figures \ref{fig1}(e) and \ref{fig1}(f).

	\section{Construction of two different double-periodic wave backgrounds  }

	In this section, we create double-periodic wave backgrounds for the Eq. (\ref{e1}) through DT formula (\ref{e3}). In the formula for one-fold DT (\ref{e3}), the seed solution $q(x,t)$ is considered to be a double-periodic wave and our task is to find its eigenvalues and eigenfunctions. To locate the eigenvalues of solutions (\ref{e4}) and (\ref{e5}), we use the nonlinearization of Lax pairs approach \cite{sinthu3,zhou}. In this approach, one can construct the solution from the knowledge of the squared eigenfunctions of Eq. (\ref{e2}) through the Bargmann constraint
	\begin{align}
		q(x,t)=\psi^2_1+\psi^2_2+\bar{\varphi}^2_1+\bar{\varphi}^2_2,
		\label{e6}
	\end{align}
	where $\psi_1$, $\psi_2$, $\bar{\varphi}_1$ and $\bar{\varphi}_2$ are the solutions of the Lax pair (\ref{s2}) at $\lambda=\lambda_1$ and $\lambda=\lambda_2$.

	The method of constructing $q(x,t)$ has already been discussed at length in the earlier works \cite{chen5}. Hence, we have skipped over those details and provide only the final expressions. Implementing the procedure, and after a very length calculation, we obtain the squared eigenfunctions $\psi^2_1$ and $\varphi^2_1$ in the form
	\begin{align}
		\label{e7}
		\psi_1^2= & \frac{\lambda_1\left(q''+2|q|^2 q+4(b+\lambda_1^2)q+2\lambda_1 q'\right)}{4(\lambda_1+\bar{\lambda}_1)(\lambda_1+\bar{\lambda}_2)(\lambda_1-\lambda_2)},\nonumber\\
		\varphi_1^2= & \frac{\lambda_1\left(\bar{q}''+2|q|^2\bar{q}+4(b+\lambda_1^2)\bar{q}-2\lambda_1 \bar{q}'\right)}{4(\lambda_1+\bar{\lambda}_1)(\lambda_1+\bar{\lambda}_2)(\lambda_1-\lambda_2)},\nonumber\\
		\psi_1\varphi_1= & -\frac{\lambda_1\left(q'\bar{q}-q\bar{q}'+2\lambda_1 (2b+2\lambda_1^2+|q|^2)\right)}{4(\lambda_1+\bar{\lambda}_1)(\lambda_1+\bar{\lambda}_2)(\lambda_1-\lambda_2)}.
	\end{align}
	\begin{figure*}[!ht]
		\begin{center}
			\begin{subfigure}{0.4\textwidth}

				\includegraphics[width=\linewidth]{13drwk09a006l1}
				\caption{}
			\end{subfigure}
			\begin{subfigure}{0.4\textwidth}

				\includegraphics[width=\linewidth]{1cpk09a006l1}
				\caption{}
			\end{subfigure}\\
			\begin{subfigure}{0.4\textwidth}

				\includegraphics[width=\linewidth]{13drwk09a006l2}
				\caption{}
			\end{subfigure}
			\begin{subfigure}{0.4\textwidth}

				\includegraphics[width=\linewidth]{1cpk09a006l2}
				\caption{}
			\end{subfigure}\\
			\begin{subfigure}{0.4\textwidth}

				\includegraphics[width=\linewidth]{13drwk09a006l3}
				\caption{}
			\end{subfigure}
			\begin{subfigure}{0.4\textwidth}

				\includegraphics[width=\linewidth]{1cpk09a006l3}
				\caption{}
			\end{subfigure}
		\end{center}
		\vspace{-0.15cm}
		\caption{The qualitative profiles of rogue waves over a double-periodic solutions (\ref{e4}) and corresponding contour plots  for Eq. (\ref{e1}) with $k=0.9$ and $\delta=0.06$. (a)-(b) $\lambda_1=\sqrt{\nu_1}$, (c)-(d) $\lambda_2=\sqrt{\nu_2}$ and (e)-(f) $\lambda_3=\sqrt{\nu_3}$. }
		\label{fig2}
	\end{figure*}

	For the double-periodic wave solution Eq. (\ref{e4}), the eigenvalues are found to be real and they read
	\begin{align}
		\lambda_1=\pm\sqrt{\nu_1},\quad
		\lambda_2=\pm\sqrt{\nu_2},\quad
		\lambda_3=\pm\sqrt{\nu_3},
		\label{ee1}
	\end{align}
	where $\nu_2=\nu_3-\nu_1$, $\nu_3=1$ and the parameter $\nu_1$ varies from zero to one.
	\begin{figure*}[!ht]
		\begin{center}
			\begin{subfigure}{0.4\textwidth}

				\includegraphics[width=\linewidth]{12dx0k09a006}
				\caption{}
			\end{subfigure}
			\begin{subfigure}{0.4\textwidth}

				\includegraphics[width=\linewidth]{12dt0k09a006}
				\caption{}
			\end{subfigure}\\
			\begin{subfigure}{0.4\textwidth}

				\includegraphics[width=\linewidth]{12dx0k09a0n006}
				\caption{}
			\end{subfigure}
			\begin{subfigure}{0.4\textwidth}

				\includegraphics[width=\linewidth]{12dt0k09n08a006}
				\caption{}
			\end{subfigure}
		\end{center}
		\vspace{-0.15cm}
		\caption{Two dimensional plots for rogue waves over a double-periodic solution (\ref{e4}) of Eq. (\ref{e1}) with $\lambda_1=\sqrt{\nu_1}$. (a) $x=0$,$k=0.9$ and $\delta=0.06$, (b) $t=0$, $k=0.9$ and $\delta=0.06$, (c) $x=0$, $k=0.9$ and two different values of $\delta$ ($0$ [blue color], $0.06$ [orange color]) and (d) $t=0$, $\delta=0.06$ and two different values of $k$ ($0.8$ [orange color],$0.9$ [blue color]).}
		\label{fig3}
	\end{figure*}

	In the case of double-periodic wave solution Eq. (\ref{e5}), we found only one eigenvalue as real and the other two turned out to be complex conjugates, that is
	\begin{align}
		\lambda_1=\pm\sqrt{\nu_1},\quad
		\lambda_2=\pm\sqrt{\alpha+i\beta},\quad \lambda_3=\pm\sqrt{\alpha-i\beta},
		\label{ee2}
	\end{align}
	where $\alpha=\frac{\nu_1}{2}$ and $\beta=\sqrt{(\frac{1}{2}-\alpha)(\frac{1}{2}+\alpha)}$.

	Once the eigenvalues and squared eigenfunctions are identified, by substituting these expressions and the double-periodic wave solutions in the onefold-DT (\ref{e3}) we can generate the waves that are in the form of periodic in both space and time and which in turn constitute the background waves for the fifth-order NLS Eq. (\ref{e1}). Our next task is to engender RWs over these double-periodic wave backgrounds. For this purpose, we proceed to establish another solution of Eq. (\ref{s2}), which is a linearly independent one.
	\begin{figure*}[!ht]
		\begin{center}
			\begin{subfigure}{0.4\textwidth}

				\includegraphics[width=\linewidth]{23drwk09a005l1}
				\caption{}
			\end{subfigure}
			\begin{subfigure}{0.4\textwidth}

				\includegraphics[width=\linewidth]{2cpk09a005l1}
				\caption{}
			\end{subfigure}\\
			\begin{subfigure}{0.4\textwidth}

				\includegraphics[width=\linewidth]{23drwk09a005l2}
				\caption{}
			\end{subfigure}
			\begin{subfigure}{0.4\textwidth}

				\includegraphics[width=\linewidth]{2cpk09a005l2}
				\caption{}
			\end{subfigure}
		\end{center}
		\vspace{-0.15cm}
		\caption{The qualitative profiles of rogue waves over a double-periodic solutions Eq. (\ref{e5}) and corresponding contour plots  for Eq. (\ref{e1}) with $k=0.9$ and $\delta=0.05$. (a)-(b) $\lambda_1=\sqrt{\nu_1}$, (c)-(d) $\lambda_2=\sqrt{\alpha+i\beta}$.}
		\label{fig4}
	\end{figure*}
	\section{Construction of RW solutions on a double-periodic wave background}

	We choose the second solution $\varphi=(\hat{\psi}_1,\hat{\varphi}_1)^{T}$ of the linear Eq. (\ref{s2}), as is given by \cite{chen5}
	\begin{align}
		\label{e8}
		\hat{\psi}_1 = \psi_1 \gamma_1-\frac{2\bar{\varphi}_1}{|\psi_1|^2+|\varphi_1|^2}, \quad \hat{\varphi}_1 =  \varphi_1 \gamma_1+\frac{2\bar{\psi}_1}{|\psi_1|^2+|\varphi_1|^2},
	\end{align}
	where $\gamma_1$ is an unknown function that must be determined.

	The explicit expression for the unknown function $\gamma_1$ can be determined from Eq. (\ref{s2}).
	Substituting Eq. (\ref{e8}) into the first equation in Eq. (\ref{s2}), we obtain
	\begin{align}
		\label{e10}
		\gamma_{1x} = D_1:= & -\frac{4(\lambda_1+\bar{\lambda}_1)\bar{\psi}_1\bar{\varphi}_1}{\left(|\hat{\psi}_1|^2+|\hat{\varphi}_1|^2\right)^2}.
	\end{align}

	Inserting Eq. (\ref{e8}) into the second equation in Eq. (\ref{s2}), we found
	\begin{align}
		\gamma_{1t} = D_2: = &\frac{2 (\lambda_1+\bar{\lambda}_1)S_1{\bar{\psi}_1}^2}{(|\psi_1|^2+|\varphi_1|^2)^2}
		+\frac{2 (\lambda_1+\bar{\lambda}_1)S_2\bar{\varphi}_1^2}{(|\psi_1|^2+|\varphi_1|^2)^2}-\frac{4 (\lambda_1+\bar{\lambda}_1)S_3\bar{\psi}_1\bar{\varphi}_1}{(|\psi_1|^2+|\varphi_1|^2)^2},
		\label{s3}
	\end{align}
	where
	\begin{align}
		S_1=~&8\delta(\lambda_1-\bar{\lambda}_1)|q|^2q+q(i+12\delta\bar{q}q_x+16\delta(\lambda_1-\bar{\lambda}_1)(\lambda_1^2+{\bar{\lambda}_1}^2))+2\delta(q_{xxx}\nonumber\\&+2(\lambda_1-\bar{\lambda}_1)q_{xx}+4(\lambda^2_1-|\lambda_1|^2+\bar{\lambda}_1^2)q_x),\nonumber\\
		S_2=~&8\delta(\lambda_1-\bar{\lambda}_1)|q|^2\bar{q}+\bar{q}(i-12\delta q\bar{q}_x+16\delta(\lambda_1-\bar{\lambda}_1)(\lambda_1^2+{\bar{\lambda}_1}^2))-2\delta(\bar{q}_{xxx}\nonumber\\&-2(\lambda_1-\bar{\lambda}_1)\bar{q}_{xx}+4(\lambda^2_1-|\lambda_1|^2+\bar{\lambda}_1^2)\bar{q}_x),\nonumber
	\end{align}
	\begin{align}
		S_3=~& i(\lambda_1-\bar{\lambda}_1)+2\delta(3|q|^4+\bar{q}q_{xx}-|q_x|^2+2(\lambda_1-\bar{\lambda}_1)\bar{q}q_x+8(\lambda_1^4-|\lambda_1|^2\times\nonumber\\&(\lambda_1^2+\bar{\lambda}_1^2)+|\lambda_1|^4+\bar{\lambda}_1^4)+q(\bar{q}_{xx}-2(\lambda_1-\bar{\lambda}_1)\bar{q}_x+4(\lambda_1^2-|\lambda_1|^2+\bar{\lambda}_1^2)\bar{q})).\nonumber
	\end{align}
	The system of first-order partial differential Eqs. (\ref{e10}) and (\ref{s3}) are compatible with each other through this relation $D_{1t}=D_{2x}$. Upon integrating Eqs. (\ref{e10}) and (\ref{s3}), we get
	\begin{align}
		\label{e12}
		\gamma_1(x,t)= & \int_{x_0}^{x} D_1(x',t_0)dx'+ \int_{t_0}^t D_2(x_0,t')dt',
	\end{align}
	where $x_0$ and $t_0$ are fixed arbitrarily. Since the functions $D_1(x,t)$ and $D_2(x,t)$ have complicated expressions we move on to solve the above Eq. (\ref{e12}), numerically.

	Replacing the second linearly independent solutions $\hat{\psi}_1$ and $\hat{\varphi}_1$, instead of the first solutions $\psi_1$ and $\varphi_1$, in the DT formula (\ref{e3}), we found
	\begin{align}
		\label{e13}
		\hat{q}(x,t)= & q(x,t)+\frac{2(\lambda_1+\bar{\lambda}_1)\hat{\psi}_1\bar{\hat{\varphi}}_1}{|\hat{\psi}_1|^2+|\hat{\varphi}_1|^2},
	\end{align}
	in which $\hat{\psi}_1$ and $\hat{\varphi}_1$ are given in Eq. (\ref{e8}). Equation (\ref{e13}) yields a novel solution for the fifth-order NLS Eq. (\ref{e1}).

	We have two families of double-periodic solutions Eqs. (\ref{e4}) and (\ref{e5}), each has a set of three eigenvalues. By substituting the double periodic solution in Eq. (\ref{e4}) with the first eigenvalue $\lambda_1=\pm\sqrt{\nu_1}$, squared eigenfunctions and also the second solution Eq. (\ref{e8}) in Eq. (\ref{e13}), we can generate the RW over a double-periodic wave background. By replacing the eigenvalues $\lambda_2$ and $\lambda_3$ separately in place of $\lambda_1$, we came across RWs with different amplitudes on the same doubly periodic wave background. A similar action with Eq. (\ref{e5}) also yield RWs of different nature.

	Figure \ref{fig2} represents the three-dimensional plots of $|\hat{q}|^2$ and their corresponding contour plots of RW over the double-periodic solution Eq. (\ref{e4}) of the fifth-order NLS Eq. (\ref{e1}) for $k=0.9$, $\delta=0.06$ and three different sets of real eigenvalues (\ref{ee1}). The RWs obtained with the background of double-periodic wave for $\lambda_1=\sqrt{\nu_1}$ ($\nu_1$ is the free parameter, which varies from $0$ to $0.5$) is illustrated in Figure \ref{fig2}(a) and its contour plot is given in Figure \ref{fig2}(b). Figures \ref{fig2}(c) and \ref{fig2}(d) which are same as Figs. \ref{fig2}(a) and \ref{fig2}(b) but drawn for $\lambda_2=\sqrt{\nu_2}$, where $\nu_2=\nu_3-\nu_1$ and $\nu_3=1$. The outcome for the eigenvalue $\lambda_3=\sqrt{\nu_3}$ is produced in Figures \ref{fig2}(e)-\ref{fig2}(f). In all the cases, we notice that the amplitude of RWs attain their highest value at the origin $(x,t)=(0,0)$. However, they differ from each other in amplitude. This is because there is a magnitude of variation in the eigenvalues. The magnitude of eigenvalues depends on the elliptic modulus parameter in the form $k=2\sqrt{\nu_1 \nu_2}$. The amplitude $|\hat{q}|^2$ varies in each case $( 11.8376<16.5893<19.1704)$ in the order of eigenvalues $\lambda_1<\lambda_2<\lambda_3$. We could also visualize changes in their orientation (see their respective contour plots).
	\begin{figure*}[!ht]
		\begin{center}
			\begin{subfigure}{0.4\textwidth}

				\includegraphics[width=\linewidth]{22dx0k09a005}
				\caption{}
			\end{subfigure}
			\begin{subfigure}{0.4\textwidth}

				\includegraphics[width=\linewidth]{22dt0k09a005}
				\caption{}
			\end{subfigure}\\
			\begin{subfigure}{0.4\textwidth}

				\includegraphics[width=\linewidth]{22dx0k09a0n005}
				\caption{}
			\end{subfigure}
			\begin{subfigure}{0.4\textwidth}

				\includegraphics[width=\linewidth]{22dt0k09n03a005}
				\caption{}
			\end{subfigure}
		\end{center}
		\vspace{-0.15cm}
		\caption{Two dimensional plots for rogue waves over a double-periodic solution (\ref{e5}) of Eq. (\ref{e1}) with $\lambda_1=\sqrt{\nu_1}$. (a) $x=0$, $k=0.9$ and $\delta=0.05$, (b) $t=0$, $k=0.9$ and $\delta=0.05$, (c) $x=0$, $k=0.9$ and two different values of $\delta$ ( $0$ [blue color], $0.05$ [orange color]) and (d) $t=0$, $\delta=0.05$ and two different values of $k$ ($0.3$ [orange color],$0.9$ [blue color]).}
		\label{fig5}
	\end{figure*}

	Two dimensional plots of $|\hat{q}|^2$ on the same background (\ref{e4}) with $\lambda_1=\sqrt{\nu_1}$ are given in Figure \ref{fig3}. For $k=0.9$ and $\delta=0.06$, the cross sectional RW pattern obtained in $t$-plane at $x=0$ is displayed in Figure \ref{fig3}(a) and a similar cross sectional wave pattern was observed in the $x$ plane at $t=0$ (Figure \ref{fig3}(b)). In both the cross sectional views, as one can see, the amplitude of the RWs attain their maximum ($\approx 12$) with different amplitudes of the background waves. In Figure \ref{fig3}(c), the RWs with double-periodic wave solution of Eq. (\ref{e1}) with $x=0$, $k=0.9$ for different values of system parameter $(\delta)$ is shown. The blue color peaks represent the two dimensional RW pattern of Eq. (\ref{e1}) with $\delta=0$, that is, it represents the RW solution in the respective background of the standard NLS equation, whereas the orange color peaks denote the RWs for $\delta=0.06$. When we vary the system parameter from $0$ to $0.06$, we observe a couple of differences that occur (Figure \ref{fig3}(c)). Firstly, the background waves amplitude decreases and there are changes in the orientation (not very much high) in the $t$-plane. Secondly, RW becomes sharp whose width narrows to lie inside the width of NLS RW. When $\delta=0.06$ and $t=0$, the RWs with the double-periodic background for two different elliptic modulus values $k=0.8$ and $k=0.9$ are shown in Figure \ref{fig3}(d). Here also, we observe some changes in the nature of the RWs. For example, the RWs amplitude decrease and also the orientation of the repeating wave patterns of the surrounding waves change as we enhance the $k$ value to $0.9$. From these observations, we conclude that the height and width of the RWs depends on the elliptic modulus ($k$) and system parameter ($\delta$) respectively. The outcome confirm that the parameters $k$ and $\delta$ control the RWs of Eq. (\ref{e1}). So these two parameters may be used to control the appearance of RWs from the experimental point of view. When replacing the eigenvalues $\lambda_2$ and $\lambda_3$ in the place of $\lambda_1$ we notice amplitude variations in each case. The other characteristics remained unchanged.

	Three dimensional RW patterns ($|\hat{q}|^2$) on the double-periodic wave background (\ref{e5}) and their contour plots are demonstrated in Figure \ref{fig4} for  $k=0.9$ and $\delta=0.05$  using the generated RWs solution of Eq. (\ref{e1}). Figures \ref{fig4}(a)-\ref{fig4}(b) are plotted for $\lambda_1=\sqrt{\nu_1}$, whereas Figures \ref{fig4}(c)-\ref{fig4}(d) are plotted with $\lambda_2=\sqrt{\alpha+i\beta}$. RWs on the considered background and their contour plots for the eigenvalue $\lambda_3$ produce the same result (Figures \ref{fig4}(c)-\ref{fig4}(d)). This is because the third eigenvalue $\lambda_3$ is the complex conjugate of $\lambda_2$. So, we did not display the outcome obtained with $\lambda_3$ separately. In all the cases presented, we behold that the maximum amplitude of RWs is observed at the origin $(x,t)=(0,0)$. As in the previous case, the RWs have different amplitudes for each eigenvalue. The amplitude $|\hat{q}|^2$ is $17.846$ for $\lambda_1$ and it is $13.7307$ for $\lambda_2$. The amplitude of the RWs from the double-periodic wave Eq. (\ref{e5}) is larger compare to the one from the solution Eq. (\ref{e4}).

	Figure \ref{fig5} shows the two dimensional plots of RWs over a double-periodic wave solution ($\ref{e5}$) for $\lambda_1=\sqrt{\nu_1}$. When $x=0$, the cross sectional view with respect to $t$ is shown in Figure \ref{fig5}(a) whereas Figure \ref{fig5}(b) presents the cross sectional view with respect to $x$ when $t=0$, in both cases the value of $\delta$ is $0.05$. Figure \ref{fig5}(c) reveals the difference between RWs on the double-periodic wave solution of NLS (Eq. (\ref{e13}) with (\ref{e5}) when $\delta=0$) and the fifth-order NLS equations (Eq. (\ref{e13}) with (\ref{e5}) when $\delta=0.05$). Here, we notice that, the RW of a fifth-order NLS solution is very sharp and it narrows (orange color) when compared to the NLS solution (blue color). Similarly, the differences that occur in the solution Eq. (\ref{e13}) with (\ref{e5}) by varying the $k$ value is shown in Fig. \ref{fig5}(d). The RW amplitude decreases once we decrease the value of $k$ from $0.9$ (blue color) to $0.3$ (orange color). In both the Figures \ref{fig5}(c) and \ref{fig5}(d) we display the changes that occur in the orientation of the background waves by changing the values $\delta$ and $k$. The solution, Eq. (\ref{e13}) with (\ref{e5}) also gives the same observation when compared to the solution Eq. (\ref{e13}) with Eq. (\ref{e4}), that is the size and reduction in width that occur in the RW due to the system parameter. The height of the RW also decrease with respect to the elliptic modulus $k$. Here also the amplitude of the RWs and the surrounding periodic waves differ in each solution. We also observed that the background waves turn out to be larger when compare to Eq. (\ref{e13}) with Eq. (\ref{e4}). We also notice a similar outcome for the other eigenvalue $\lambda_2$. The only difference is the RW amplitude.

	It has been shown that the creation of RWs are linked to the MI of the wave backgrounds \cite{na1,jms}. In the literature, several works have been reported on RWs and the MI of the background wave for the NLS family of equations \cite{chen4,bdec}. Motivated by the above studies, in the following section, we use the linear stability analysis to study the MI of the two different double-periodic waves and evaluate the rate of instability of two different double-periodic solutions of the fifth-order NLS Eq. (\ref{e1}).

	\section{Instability rate of the two different double-periodic waves of Eq. (\ref{e1})}
	In this section, we calculate the  growth rate for instability of both the double-periodic waves, Eqs. (\ref{e4}) and (\ref{e5}), of Eq. (\ref{e1}). To determine the perturbation relation for calculating the MI growth rate, we derive two (unperturbed  and perturbed) sets of linearized equations. First, we derive a set of linearized equations for the unperturbed part and then we derive the perturbed part equations. By comparing these two set of parts linearized equations we obtain the perturbation relation. To set up the unperturbed set of linearized equation we recast the Eqs. (\ref{e4}) and (\ref{e5}) in the following form
	\begin{align}
		q(x,t)=g(x,t)~e^{2i a t},\quad g(x+\omega_1,t)=g(x,t+\omega_2)=g(x,t),
		\label{e14}
	\end{align}
	in which the fundamental period in space and time coordinate are $\omega_1>0$ and $\omega_2>0$ respectively and one might consider $2a=1$ for Eq. (\ref{e4}) and $2a= k$ for Eq. (\ref{e5}).

	The solutions, Eqs. (\ref{e4}) and (\ref{e5}) have been rewritten in a generalized form given in Eq. (\ref{e14}), with $g(x,t)$ considered as the solution of the linear equation (\ref{s2}) with $g_1$ and $g_2$, which are given by
	\begin{align}
		g_1(x,t)=&\rho_1(x,t)~e^{\eta x+(\xi+i a ) t},\nonumber\\ g_2(x,t)=&\rho_2(x,t)~e^{\eta x+(\xi-i a ) t},
		\label{e20}
	\end{align}
	where $\eta$, $\xi$ are spectral parameters and $\rho=(\rho_1,\rho_2)^T$. Substituting Eq. (\ref{e20}) into (\ref{s2}), we obtain a system of equations, namely
	\begin{subequations}
		\label{e21}
		\begin{align}
			\rho_x+\eta \rho=\begin{pmatrix}
				\lambda & g\\
				-\bar{g} & -\lambda
			\end{pmatrix}\rho,
			\label{e22}\\
			\rho_t+\xi\rho=\begin{pmatrix}
				\hat{A}_1- ia & \hat{B}_1\\
				\hat{C}_1 & -\hat{A}_1+ ia
			\end{pmatrix}\rho,
			\label{e23}
		\end{align}
	\end{subequations}
	where,
	\begin{align}
		\hat{A}_1=\;&i\left(\lambda^2+\frac{|g|^2}{2}\right)+\delta(\bar{g}g_{xxx}-g\bar{g}_{xxx}+g_x\bar{g}_{xx}-\bar{g}_xg_{xx}+6|g|^2\bar{g}g_x-6|g|^2\bar{g}_xg)\nonumber\\&+2\lambda\delta(g\bar{g}_{xx}+\bar{g}g_{xx}-|g_x|^2+3|g|^4)-4\lambda^2\delta(g\bar{g}_x-\bar{g}g_x)+8\lambda^3\delta|g|^2+16\lambda^5\delta,\nonumber\\
		\hat{B}_1=&\;i\left(\lambda g+\frac{g_x}{2}\right)+\delta(g_{xxxx}+8|g|^2g_{xxx}+2g^2\bar{g}_{xx}+4|g_x|^2g+6\bar{g}g^2_x+6|g|^4g)\nonumber\\&+2\lambda\delta(g_{xxx}+6|g|^2g_x)+4\lambda^2\delta(g_{xx}+2|g|^2g)+8\lambda^3\delta g_x+16\lambda^4\delta g,\nonumber\\
		\hat{C}_1=&\;-i\left(\lambda\bar{g}-\frac{\bar{g}_x}{2}\right)-\delta(\bar{g}_{xxxx}+8|g|^2\bar{g}_{xx}+2\bar{g}^2g_{xx}+4|g_x|^2\bar{g}+6g\bar{g}^2_x+6|g|^4\bar{g})\nonumber\\&+2\lambda\delta(\bar{g}_{xxx}+6|g|^2\bar{g}_x)-4\lambda^2\delta(\bar{g}_{xx}+2|g|^2\bar{g})+8\lambda^3\delta\bar{g}_x-16\lambda^4\delta\bar{g},\nonumber
	\end{align}

	Upon perturbing the solution  (\ref{e14}) linearly,
	\begin{align}
		q(x,t)=g(x,t)e^{2iat}+p(x,t)~e^{2iat},
		\label{e15}
	\end{align}
	where $p(x,t)$ is a function of its arguments and substituting the latter expression into (\ref{e1}) and leaving out the quadratic and cubic terms in $p$, we arrive at
	\begin{subequations}
		\label{s224}
		\begin{align}
			\label{e16}
			&ip_t-2ap+\frac{1}{2}p_{xx}+2|g|p+g^2\bar{p}-i\delta(p_{xxxxx}+10(\bar{g}p+\bar{p}g)g_{xxx}+10|g|^2p_{xxx}\nonumber\\&+10(pg_x+gp_x )\bar{g}_{xx}+10(p\bar{g}_x+g\bar{p}_x)g_{xx}+20(\bar{p}g_x +\bar{g}p_x)g_{xx}+10gg_x\bar{p}_{xx}\nonumber\\&+10(g\bar{g}_x+2\bar{g}g_x)p_{xx}+20|g_x|^2p_x+10g_x^2\bar{p}_x+60(\bar{g}p+g\bar{p})|g|^2g_x+|g|^4p_x)=0.\\
			&i\bar{p}_t-2a\bar{p}+\frac{1}{2}\bar{p}_{xx}+2|g|\bar{p}+\bar{g}^2p+i\delta(\bar{p}_{xxxxx}+10(g\bar{p}+p\bar{g})\bar{g}_{xxx}+10|g|^2\bar{p}_{xxx}\nonumber\\&+10(\bar{p}\bar{g}_x+\bar{g}\bar{p}_x )g_{xx}+10(\bar{p}g_x+\bar{g}p_x)\bar{g}_{xx}+20(p\bar{g}_x +g\bar{p}_x)\bar{g}_{xx}+10\bar{g}\bar{g}_xp_{xx}\nonumber\\&+10(\bar{g}g_x+2g\bar{g}_x)\bar{p}_{xx}+20|g_x|^2\bar{p}_x+10\bar{g}_x^2p_x+60(g\bar{p}+\bar{g}p)|g|^2\bar{g}_x+|g|^4\bar{p}_x)=0.
		\end{align}
	\end{subequations}

	We consider a simple nontrivial separable solution of Eq. (\ref{s224}) in the form
	\begin{align}
		p(x,t)=n_1(x)~e^{ \Lambda t}, \quad \bar{p}(x,t)=n_2(x)~e^{\Lambda t},
		\label{e17}
	\end{align}
	where $n_1$ and $n_2$ are the functions of $x$  ($n(x)=(n_1(x),n_2(x))^{T}$) and $\Lambda$ denotes the spectral parameter. By using Eqs. (\ref{e16}) and (\ref{e17}) we rewrite the spectral stability problem as follows,
	\begin{align}
		\label{e18}
		i\Lambda\sigma_3 ~n+\begin{pmatrix} m_{11} & m_{21}\\ \bar{m}_{21} & \bar{m}_{11} \end{pmatrix}n=0, \quad
		\sigma_3 = \begin{pmatrix}
			1 & 0 \\
			0 & -1
		\end{pmatrix},
	\end{align}
	with
	\begin{subequations}
		\label{e19}
		\begin{align}
			m_{11}=&-2a+2|f|^2+\frac{1}{2}\partial_{xx}-i\delta(|g|^4\partial_x+60|g|^2\bar{g}g_x+20|g_x|^2\partial_x+20\bar{g}g_x\partial_{xx}\nonumber\\&+10g\bar{g}_x\partial_{xx}+20\bar{g}g_{xx}\partial_x+10\bar{g}_xg_{xx}+10g\bar{g}_{xx}+10g_x\bar{g}_{xx}+10|g|^2\partial_{xxx}\nonumber\\&+10\bar{g}g_{xxx}+\partial_{xxxxx}), \\
			m_{21}=~&g^2-i\delta(10gg_{xxx}+20g_xg_{xx}+10gg_{xx}\partial_x+10gg_{xx}\partial_{xx}+10g_x^2\partial_x\nonumber\\&+60|g|^2gg_x).
		\end{align}
	\end{subequations}
	Equation (\ref{e18}) is obtained through the perturbed solution. Now comparing Eq. (\ref{e18}) with Eq. (\ref{e23}) we could fix the bounded squared eigenvalues $\rho_1^2$ and $\rho_2^2$, as $n_1=\rho_1^2$, $n_2=-\rho_2^2$ and $\delta=i\delta$. We also obtain a relationship between the spectral parameters $\Lambda$ and $\xi$ in the form $\Lambda=2\xi$ by comparing the Eqs. (\ref{e18}) and (\ref{e23}). In another words, when substituting the obtained relations, $\delta$ and $\Lambda$, in Eq. (\ref{e18}) we arrive at Eq. (\ref{e23}).

	The explicit expression for $\xi$ can be obtained from Eq. (\ref{e23}). The spectral problem or the coefficient matrix given in Eq. (\ref{e23}), provides a set of linear algebraic equations. A nonzero solution of these equations could be determined only when the determinant is zero for the coefficient matrix. This condition establish a connection between $\xi$ and $\lambda$, that is
	\begin{align}
		\xi^2+\tilde{W}(\lambda)=0,
		\label{e25}
	\end{align}
	with
	\begin{align}
		\tilde{W}(\lambda)=\lambda^4-2a\lambda^2+a^2+2b, \quad	|g_x|^2+|g|^4-4a|g|^2=8b.
		\label{e26}
	\end{align}
	\begin{figure*}[!ht]
		\begin{center}
			\begin{subfigure}{0.4\textwidth}

				\includegraphics[width=\linewidth]{1mifonls}
				\caption{}
			\end{subfigure}
			\begin{subfigure}{0.4\textwidth}

				\includegraphics[width=\linewidth]{2mifonls}
				\caption{}
			\end{subfigure}
		\end{center}
		\vspace{-0.15cm}
		\caption{Instability rate for the double-periodic waves for different elliptic modulus values with $\delta=0.01$: (a) for Eq. (\ref{e4}), (blue, green, red, pink colors denotes the different values of $k$, which are $0.999$, $0.9$, $0.7$ and $0.5$ respectively) and (b) Instability rate for Eq. (\ref{e5}) (blue, green, red, pink colors denotes the different values of $k$, which are $0.999$, $0.9$, $0.3$ and $0.2$ respectively). }
		\label{fig6}
	\end{figure*}

	The polynomial $\tilde{W}(\lambda)$ could be rewritten as
	\begin{align}
		\tilde{W}(\lambda)=\lambda^4-\frac{1}{2}(g_1^2+g_2^2)\lambda^2+\frac{1}{16}(g_1^2-g_2^2),
		\label{e28}
	\end{align}
	with $4a=g_1^2+g_2^2$ and $8b=-g_1^2g_2^2$. The roots of the polynomial $\tilde{W}(\lambda)$ are $\pm\lambda_1$ and $\pm\lambda_2$. The polynomial $\tilde{W}(\lambda)$ have two positive roots which are
	\begin{align}
		\lambda_1=\frac{1}{2}(g_1+g_2), \quad \lambda_2=\frac{1}{2}(g_1-g_2).
		\label{e29}
	\end{align}
	Using Eq. (\ref{e29}) we rewrite Eq. (\ref{e28}) in the form
	\begin{align}
		\tilde{W}(\lambda)=(\lambda^2-\lambda_1^2)(\lambda^2-\lambda_2^2).
		\label{e30}
	\end{align}
	From Eq. (\ref{e28}), we get a relationship between $\xi$ and $\lambda_i$'s in the following form
	\begin{align}
		\xi=\pm i\sqrt{(\lambda^2-\lambda_1^2)(\lambda^2-\lambda_2^2)}
		\label{e32}
	\end{align}

	With the help of Eq. (\ref{e32}), we rewrite the value of $\Lambda$ in the form
	\begin{align}
		\Lambda=\pm 2i\sqrt{(\lambda^2-\lambda_1^2)(\lambda^2-\lambda_2^2)}\quad \text{or}\quad \Lambda=2\xi,
	\end{align}
	where the values of $\lambda$, could be obtained from the spectral problem (\ref{e22}), that is
	\begin{equation}
		\begin{pmatrix} \frac{d}{dx}+\eta & -g\\ -\bar{g} & -\frac{d}{dx}-\eta \end{pmatrix}\begin{pmatrix} \rho_1\\ \rho_2 \end{pmatrix}=\lambda \begin{pmatrix} \rho_1\\ \rho_2 \end{pmatrix},
		\label{e31}
	\end{equation}
	where $\eta=i\theta$ and the Floquet parameter, $\theta\in(0,\frac{\pi}{\omega_1})$. We solve Eq. (\ref{e31}), through numerically, using the eigenvalue solver technique \cite{chen1,dep}. Using the relation $\Lambda$, we can compute the instability rate of the considered system. In the numerical plotting part we consider the values of $\Lambda$ and $\delta$ are real.

	Instability rate of the two double-periodic waves (\ref{e4}) and (\ref{e5}) for the fifth-order NLS equation is illustrated in Figure \ref{fig6} with four different $k$ values with $\delta=0.01$. Here, $Re(\Lambda)$ is plotted against $\theta$, where the $\theta$ value is considered between the range $0$ to $\frac{\pi}{\omega_1}$. The highest instability rate of Eq. (\ref{e4}) is achieved when $k=0.999$ and this maximal instability rate decrease when the value of $k$ is decreased from $0.999$ to $0.5$ (Figure \ref{fig6}(a)). For $k=0$ the double-periodic solutions, Eqs. (\ref{e4}) and (\ref{e5}) converge to the NLS soliton and cnoidal wave, respectively and for $k=1$, the spectrum of both the solutions achieve Akhmediev breathers level. In Figure \ref{fig6}(b) we display the rate of instability for the double-periodic wave of Eq. (\ref{e5}). Here also the highest instability rate is obtained for $k=0.999$ ($k\approx1$). The instability rate decrease when $k$ value is decreased from higher ($0.999$) to lower ($0.3$). Further, when we decrease the value of elliptic modulus say $k=0.2$, the maximal instability suddenly increase but it is lesser than the $k=0.9$ curve. From Figure \ref{fig6}, we observe that both the double-periodic waves, the instability rate attained its maximal level to $0.999$ ($\approx 1$) and width of the spectrum also had the same range $0.7$. This is because, both the solutions converge to Akhmediev breathers when $k=1$. In both the solutions, the largest instability rate and the width of them gradually decrease when the system parameter ($\delta$) value is increased.
	\section{Conclusion}
	We investigated the RW solution with two different double-periodic wave backgrounds for the fifth-order NLS equation through DT. The approach of nonlinearization of the Lax pair or spectral problem was used to estimate eigenvalues and squared eigenfunctions associated with these double-periodic wave solutions. We constructed two different backgrounds that are periodic in both space and time by substituting the derived eigenvalues, squared eigenfunctions and the double-periodic seed solution into the DT (\ref{e3}). We then created the RWs over the constructed wave backgrounds by using the second linearly independent solution (which is of a non-periodic form and grows linearly on $x$ and $t$) to the Lax pair equation. We investigated the characteristics of RWs for various system parameter values $(\delta)$ and for the different eigenvalues. We observed that the orientation and the number of occurrences of repeating wave patterns of both the double-periodic wave changes in both space and time axis. We also noticed that the double-periodic waves and the RWs amplitude varies depending on its eigenvalues. To get a better understanding of these RWs over the double-periodic wave background, we drew two dimensional plots for two different values of system and elliptic modulus parameters. These figures brought out the differences between the RW structures in the basic NLS equation and its higher-order variant, say fifth-order NLS equation. In the case of higher-order NLS, the RWs are very sharp and it narrows inside the NLS RW due to higher-order dispersion effects. We also noticed that, by decreasing the value of $k$, the height of the RWs for both double-periodic wave solutions decreases. Hence, we concluded that the parameters $\delta$ and $k$ can be used to analyze the appearance/disappearance of RWs in several oceanographic and hydrodynamics experiments. We also calculated the growth rate for instability of both the double-periodic waves for the fifth-order NLS equation using the spectral stability analysis method. By perturbing the double-periodic wave solutions linearly and substituting this into the fifth-order NLS equation, we obtained a set of linearized equations. Upon solving this set of linearized equations, we obtained the instability relations. Finally, we computed the instability rate for a particular value of the system parameter and examined the rate of instability for four different values of  elliptic modulus parameter. Furthermore, RWs on a double-periodic wave background have a wide range of applications in mathematics and physics \cite{rand,kim}. The results of our paper may prove to be useful for diagnosing RWs on the surface of the ocean and understanding how random waves form, owing to MI \cite{ac1}.
	\section*{Acknowledgements}
	NS wishes to thank MoE-RUSA $2.0$ Physical Sciences, Government of India for sponsoring a fellowship for this research work. MS acknowledges MoE-RUSA $2.0$ Physical Sciences, Government of India for sponsoring this research work. MS also acknowledges the research project sponsored by NBHM, Government of India, under the Grant No. $02011/20/2018$ NBHM(R.P)/R$\&$D II/$15064$.

redpajama_set_name: RedPajamaArXiv


Beautiful home for the ultimate outdoor family or company. It features a spacious main house, guest house, a beautiful waterfront pasture, and access to the best hunting and fishing in Idaho. Located right on Idaho's famous Salmon River.


text:
Colayo
Bani § Barangays
Colayo, Municipality of Bani, Province of Pangasinan
16.2754, 119.8099 (16° 17' North, 119° 49' East)
152.5 meters (500.3 feet)
Colayo is a barangay in the municipality of Bani, in the province of Pangasinan. Its population as determined by the 2020 Census was 2,131. This represented 4.05% of the total population of Bani.
The household population of Colayo in the 2015 Census was 1,900 broken down into 497 households or an average of 3.82 members per household.
Number of households in Colayo (1990‑2015)
According to the 2015 Census, the age group with the highest population in Colayo is 5 to 9, with 228 individuals. Conversely, the age group with the lowest population is 75 to 79, with 24 individuals.
Population of Colayo by age group (2015 census)
Youth Dependency Ratio: 56.78
Old Age Dependency Ratio: 11.51
The population of Colayo grew from 1,279 in 1990 to 2,131 in 2020, an increase of 852 people over the course of 30 years. The latest census figures in 2020 denote a positive growth rate of 2.44%, or an increase of 231 people, from the previous population of 1,900 in 2015.
Population of Colayo (1990‑2020)
1,280 -0.18%
Colayo is situated at approximately 16.2754, 119.8099, in the island of Luzon. Elevation at these coordinates is estimated at 152.5 meters or 500.3 feet above mean sea level.
Colayo shares a common border with the following barangay(s):
Centro Toma, Bani, Pangasinan
Macabit, Bani, Pangasinan
Catuday, Bolinao, Pangasinan

redpajama_set_name: RedPajamaCommonCrawl


The Castle was built in 1270 and was the childhood home of Anne Boleyn who became queen when she married King Henry VIII in 1533. As his second wife she ended up being beheaded, poor woman! The Castle itself is beautiful and inside most of the rooms have been restored to what they once looked like. In each room there are models, tapestries, antiques, furniture and reconstructed stories of the past.
As well as Anne Boleyn's bedroom there is also the bedchamber where it is believed that Henry VIII stayed in when visiting. To keep the kids amused there was also an Easter Bunny Hunt in every single room where children had to find the hidden bunny. Despite no prize at the end, Pip had a great time spotting the bunny in a cabinet display or sometimes on the shoulders of King Henry VIII (in the photo above)! Spot the bunny in the photo below too!
The grounds of Hever Castle are just as stunning and it's worth visiting just for them! There are 125 acres of grounds across Hever Castle and this includes the beautiful views across the lake and Italian, Rose and Tudor gardens.
We visited the maze just outside the castle which is actually the first maze Pip has ever entered! Although we completed one Easter hunt in the castle the kids were keen to do the outside carrot trail Easter hunt where we had to find and count the carrots hidden around the grounds. From the Castle we walked down to the lake, walking through the Italian Garden on the way. With Italian features including a Pompeiian Wall, Sunken Garden and a Loggia complete with colonnades and a piazza all surrounded by beautiful flowers, you would not know you were in England at all! In fact, I would return for this garden alone. It is stunning and bought back lots of memories of Italy. Next to the lake this is also a fountain inspired by the famous Trevi Fountain in Rome!
Apart from the Easter hunts, Castle & Lake we also visited the three activity areas for children. They are located next to one another near to the main entrance. The Acorn Dell is a natural play area including a giant sandpit, grassy mound, tunnels, climbing frame and slide. Next door is the Tudor Towers Adventure Playground which is a big wooden structure that kids can run around in. Next door is another outdoor playground with swings, slide and climbing frame.
At the end of the day we visited the gift shop and inside is the intriguing gallery of miniature model houses. I loved these and Pip was fascinated by them. Inside each house model contained the most intricately designed miniature people and furniture. It was amazing to appear into these little models of reconstructed life. I'm sure this gallery would appeal to all Doll's House enthusiasts!
All in all we had a lovely day out and there was a lot more to Hever Castle than I imagined. We didn't have time to visit the KSY military museum, the Japanese Tea House or take the long walk around the lake but it would be great to visit again in the summer. The Easter Family Fun runs until 22 April and includes the Castle Bunny Hunt, Colourful Carrots Easter Hunt, face painting, Bonnet Making Workshop and the Best Bonnet Competition. There are also events throughout the year including the May Day Festival, Father's Day Weekend, Jousting events and more. See their website for more details.
The best cities to visit in England!
* Many thanks to Hever Castle for providing guest tickets! This is a sponsored post. All words and opinions are my own.


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text:
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#include "V8Node.h"
#include "V8Utilities.h"
#include "WebDevToolsFrontendClient.h"
#include "WebFrameImpl.h"
#include "WebScriptSource.h"
#include "WebViewImpl.h"
#include <wtf/OwnPtr.h>
#include <wtf/Vector.h>
#include <wtf/text/WTFString.h>

using namespace WebCore;

namespace WebKit {

static v8::Local<v8::String> ToV8String(const String& s)
{
    if (s.isNull())
        return v8::Local<v8::String>();

    return v8::String::New(reinterpret_cast<const uint16_t*>(s.characters()), s.length());
}

WebDevToolsFrontend* WebDevToolsFrontend::create(
    WebView* view,
    WebDevToolsFrontendClient* client,
    const WebString& applicationLocale)
{
    return new WebDevToolsFrontendImpl(
      static_cast<WebViewImpl*>(view),
      client,
      applicationLocale);
}

WebDevToolsFrontendImpl::WebDevToolsFrontendImpl(
    WebViewImpl* webViewImpl,
    WebDevToolsFrontendClient* client,
    const String& applicationLocale)
    : m_webViewImpl(webViewImpl)
    , m_client(client)
    , m_applicationLocale(applicationLocale)
{
    InspectorController* ic = m_webViewImpl->page()->inspectorController();
    ic->setInspectorFrontendClient(adoptPtr(new InspectorFrontendClientImpl(m_webViewImpl->page(), m_client, this)));

    // Put each DevTools frontend Page into its own (single page) group so that it's not
    // deferred along with the inspected page.
    m_webViewImpl->page()->setGroupName(String());
}

WebDevToolsFrontendImpl::~WebDevToolsFrontendImpl()
{
}

void WebDevToolsFrontendImpl::dispatchOnInspectorFrontend(const WebString& message)
{
    WebFrameImpl* frame = m_webViewImpl->mainFrameImpl();
    v8::HandleScope scope;
    v8::Handle<v8::Context> frameContext = frame->frame() ? frame->frame()->script()->currentWorldContext() : v8::Local<v8::Context>();
    v8::Context::Scope contextScope(frameContext);
    v8::Handle<v8::Value> inspectorFrontendApiValue = frameContext->Global()->Get(v8::String::New("InspectorFrontendAPI"));
    if (!inspectorFrontendApiValue->IsObject())
        return;
    v8::Handle<v8::Object> inspectorFrontendApi = v8::Handle<v8::Object>::Cast(inspectorFrontendApiValue);
    v8::Handle<v8::Value> dispatchFunction = inspectorFrontendApi->Get(v8::String::New("dispatchMessage"));
     // The frame might have navigated away from the front-end page (which is still weird).
    if (!dispatchFunction->IsFunction())
        return;
    v8::Handle<v8::Function> function = v8::Handle<v8::Function>::Cast(dispatchFunction);
    Vector< v8::Handle<v8::Value> > args;
    args.append(ToV8String(message));
    v8::TryCatch tryCatch;
    tryCatch.SetVerbose(true);
    ScriptController::callFunctionWithInstrumentation(frame->frame() ? frame->frame()->document() : 0, function, inspectorFrontendApi, args.size(), args.data());
}

} // namespace WebKit

redpajama_set_name: RedPajamaGithub


I visited Paris during the third weekend in October and I felt like I was tunneling through an iceberg the entire the time. That might be a slight exaggeration and , granted, I am the one with a cardigan in the middle of July, but it was pretty darn cold. Everyone was bundled up in padded winter jackets and hats pulled down low. I stepped off the plane with only a thin sweater and decorative scarf. Thank goodness for the H&M I accidentally stumbled upon. I was able to buy a decent winter jacket for less than 30 Euros. I wore it well into spring and it looks good enough to make a reprise this winter.
Every major city has traffic lights but traffic patterns defiantly differ from place to place. That's something I had to learn the hard way. In Paris, that meant running into a lane of traffic , thinking I was running out of the line of fire. It was a quick crash course on Parisian traffic but I'll never forget the look of hatred on that bus driver's face.
Paris is known as one of the most expensive cities in the world. While it certainly has the possibility to live up to that title, there are numerous discounts for the student to take advantage of. Pretty much every attraction I visited, like the Eiffel Tower and The Louvre Museum, were discounted or free by showing my student ID.
Another common stereotype labels Paris as extremely unfriendly. I've read and heard first hand accounts of the rudeness shown to travelers and was a bit worried in the days leading up to the trip. It turns out , there was no need to stress. With the exception the security guards at Le Zenith and whoever stole my Bruno Mars concert shirt, people in Paris were remarkable friendly and conversational. Multiple people stopped to give detailed directions or recommendations and we were normally greeted with smiles when walking into a shop or restaurant. I found that attempting a few words of French , whether it was Bonjour, Parlez vous anglais, or Merci ,made it much easier to approach people and get a positive response.
Simply put, Paris was one of the most beautiful places I was fortunate enough to experience first-hand. Around every corner was the outline of another stately and historic building. The streets were either cobble stoned or marked by neat, uniform lines of both vintage and designer stores. Of course, there are few scenarios more picturesque that walking along the Seine River and blinking at the tower in the distance.


"This was hilarious! Well thought out & extremely humorous!"
Bernie Madoff and his partner Barack Obama stood on one side of the cage, quietly eyeing their opponents a few feet away. Likewise, O. J. Simpson and George Clooney said nothing, but had looks of grim determination on their faces. Even ebullient ringmaster Bruce Buffer couldn't muster much bravado during the announcement. This was no ordinary cage match. For one thing, it was the first tag team cage match in UFC history. Also, two highly advanced, competing alien races had just conquered Earth, and were using the match as a way to decide which will earn dominion over the planet.
The Rabsnitx are methane breathing miners who specialize in dissecting planets for the raw materials. If their team, Simpson and Clooney, are victorious, within a few weeks, the entire planet will be dismantled and shipped through a wormhole to another part of the galaxy. The Rabsnitx are not known for showing concern for indigenous species when they conduct their business. When the anti-gravity modules are turned on, anything not attached to the surface of the planet ends up in outer space, freeze dried, within a few seconds.
The Wal'slerth are a wealthy species, due to their success at developing exotic vacation packages all over the galaxy. They are innately optimistic herbivores and are already planning their advertising campaign. The geyser pools at Yellowstone will be a desirable stop for the various non-feathered races from the Orion Belt. The more acidic the water, the better. Sentient varieties of what humans would think of as algae will pay outrageous prices to leisurely engage in binary fission in the damp recesses of Carlsbad Caverns.
They learned eons ago, planets that are maintained in pristine, native condition are the most sought after as vacation spots. The supply ships that will descend on Earth if Madoff and Obama win will bring technology humans have never imagined. Extinct species will flourish, pollution will disappear, earthquakes and destructive weather patterns will be tamed. The human race will be educated, fed, and trained to be gracious hosts. Poverty, disease and war will no longer exist. Earth will become a welcoming paradise for all forms of life, native and alien.
Given the circumstances, you might ask why Simpson and Clooney wouldn't simply throw the match. The galactic community has been through this before and the details have been refined for eons. Backwards humans are no match for the mind control technology the Rabsnitx are fond of using. They scanned all 7 billion humans and identified four whose species survival instincts could be overpowered by minor chemical tweaks to their already massive egos. Plus, by intergalactic tag team cage fighting rules, the match will not end until a member of the losing team is dead.
So when Big John McCarthy shouted, "Let's get it on", the fate of the human race and its home planet hung in the balance. To start off, it was Obama against Clooney. After the two exchanged some jabs, the Russian attempted a takedown. Obama sprawled and got an arm around Clooney's neck. The two went down to the mat and Obama began to work around to mount Clooney's back. Clooney saw what was happening and used his superior strength to move both men toward Simpson's outstretched hand, and tagged out.
Obama also took the opportunity to tag out, so now it was Madoff against Simpson. At first, Simpson took advantage of his edge in athleticism. He bobbed left and right and began pummeling the financier with fists, elbows and knees. But one thing you can't measure in a fight is a man's heart. Madoff weathered the initial storm, and when Simpson showed signs of tiring, he went on the offensive. Bernie delivered a series of leg kicks that were brutal enough to knock Simpson to the ground several times. The kicks began to stunt O.J.'s mobility. Madoff began to pepper his opponent's face with jab after jab. Sensing impending unconsciousness, Simpson tagged out.
Clooney came in fresh, but by now Bernie was fighting like a man possessed by the Devil. The punches and kicks continued nonstop for several minutes, and when Clooney fell to the floor in a defensive position, Madoff took his back and sunk in a rear naked choke. Clooney's face turned red, after a few seconds, he began tapping. But this was a fight to the death, Big John did not stop the fight when Clooney tried to surrender.
The crowd of aliens had been making noise ever since the start of the match. Methane breathers expel gasses through a vent. When they get excited, it sounds like a kazoo. Wal'slerth have what we would describe as high tech horseshoes attached to their hooves, they click those together the same way humans clap their hands. The Mandalay Bay Event Center was filled with thousands of kazoo playing Rabsnitx who were accompanied by a similar number of sentient zebras playing percussion. It was Metallica loud and unlike any sound ever heard by human ears.
But when Madoff let go of Clooney and stood up, the aliens went silent. Clearly, Clooney was not dead yet. His chest heaved as he lay on the ground. This was unprecedented. The aliens were certain the humans had been given proper instructions on how to finish the match.
The stunned silence continued. The aliens were baffled. It turns out that, regardless of the advanced science and fantastic technology the many galactic races had developed, regardless of how many billions of years these races had roamed the heavens, there was something they had never encountered before. One characteristic that, out of billions of life forms, had only evolved on Earth. One thing that set humans apart from every other species in the universe. That quality is free will.
When the aliens experienced this new concept for the first time, it scared the crap out of them. The Rabsnitx emptied the arena in silence. Obama's cell phone buzzed, it was a text from their ambassador. Due to an unexpected drop in the price of metals, the mining of Earth was no longer economically feasible. The Rabsnitx vessels will not be returning to this backwater sector of the galaxy.
So that's how we finally got rid of Bernie Madoff and O.J. Simpson. If things work out, those two will mess up the rest of the galaxy so bad, we'll never see them or any aliens again.
QUESTION: How come the aliens got Madoff and Simpson while the Earth got Putin and Obama?
ANSWER: They flipped a coin, and the aliens won the toss.
Whiskey, I just experienced what the young folks would describe as LMFAO.
Hah! Well that was entertaining. I wonder how long it would take O.J to make the aliens realize they have made a horrible mistake. I liked how you described the cage matches. I could picture them perfectly and I got a good laugh.
Thanks. I can't imagine aliens anywhere wanting anything to do with us.
This was hilarious! Well thought out & extremely humorous!
Thanks, I appreciate the read and the comment.


Geosciences professor Julie Libarkin doesn't wear dresses in public.
It's not because she has to get down on the ground to do her job — she doesn't dig up rocks — but because she cannot stand the constant harassment that comes when she does.
"I don't wear dresses any more because almost every time I have worn a dress, I have been assaulted," said Libarkin, who is now a full professor at of Michigan State University.
Libarkin is far from alone. More than half — 58 percent — of women in academia have been sexually harassed, the the National Academies of Sciences, Engineering, and Medicine (NASEM) says in a new report.
That makes academia second only to the military in terms of rates of sexual harassment. Nearly 70 percent of military women say they've been sexually harassed.
Science, technology, engineering and medicine (STEM) fields are the worst, the report finds.
It lays down a road map for universities and other academic institutions to do something about it.
"Through our work it became clear that sexual harassment is a serious issue for women at all levels in academic science, engineering, and medicine, and that these fields share characteristics that create conditions that make harassment more likely to occur," the study group's co-chairs, Wellesley College president Paula Johnson and Massachusetts Institute of Technology professor Sheila Widnall wrote in the report's introduction.
Concrete ways to help make it stop include sending a clear message that harassment will not be tolerated; supporting women who report incidents; making investigations clear and open; and diluting the power of male superstars, who often control the careers of everyone below them.
Libarkin approves of this proposal. Academic careers often hinge on a single mentor, and that's not good for men or women, she said.
"I would suggest that even before entering STEM, (women) use social media to build a community of people," said Libarkin, who heads the Geocognition Research Lab at Michigan State University.
Academia is especially prone to sexual harassment because of the hierarchical nature of institutions, the report says.
And of course, most universities and colleges are male-dominated.
"Most department chairs and deans are men. Most principal investigators are men. Most provosts and presidents are men," the report reads.
That doesn't mean that all men harass all women, but it's clear that when there's a boy's club atmosphere, with tacit signals that sexual harassment or discrimination will be winked at, bad behavior flourishes.
It's so bad that women have started an online community to share their experiences.
Jen, who did not want to use her real name, said she suffered after she quietly asked a colleague to stop verbally harassing her.
"He must have complained," she wrote on the #MeTooSTEM blog.
"Lily" says she was raped and has suffered pervasive sexual harassment, but says her worst moment was when her academic adviser asked her to be 'the estrogen in the room' at a meeting.
"He didn't ask me to go because of my strong communication and negotiation skills, or because of the work I'd done leading up to this moment, or because I was co-managing the project. He asked me to go because I was a girl," she wrote.
This kind of behavior must stop, the NASEM report says.
"Academic institutions should be as transparent as possible about how they are handling reports of sexual harassment," the report reads. Cover-ups make things worse.
"Academic institutions should consider power-diffusion mechanisms (i.e., mentoring networks or committee-based advising and departmental funding rather than funding only from a principal investigator) to reduce the risk of sexual harassment," it adds.
And women who report harassment should be treated as "honorable and courageous," not as trouble-makers.
Having to battle sexual harassment is wasting time and money, the report said. And it's costing society when women drop promising careers — or fail to even pursue them.
"What is especially discouraging about this situation is that at the same time that so much energy and money is being invested in efforts to attract and retain women in science, engineering, and medical fields, it appears women are often bullied or harassed out of career pathways in these fields," the report reads.
Libarkin said she cannot even guess how much work she has lost because of the harassment she has experienced.
"This stuff takes an inordinate amount of time," Libarkin said.
Libarkin says the report is a good first step. Institutions also must address discrimination and harassment of ethnic and other minorities, she said.
And the National Academies are highly respected, even if the organization is advisory only.
"One of my colleagues pointed out that of course the report has no teeth," she said.


text:
For 40 years, Modern Communications' mission has been to provide full-service,
cutting-edge technology solutions, while delivering a world-class experience
for our partners.
In August of 1978, Don Johnson founded Modern Communications with an aim to sell Patient Education
Programs to hospitals and other medical centers in the Greater St. Louis Area. At that time, Modern employed
just one person, Don's brother, Bill, who served as the Company's first employee. The two-man team worked tirelessly, out of a small office in Crestwood, MO to establish a solid foundation for a business that now serves as a leading provider of state-of-the-art technology solutions across Missouri and Southern Illinois.
Soon after their founding, Bill came to understand that hospitals and medical centers had more of an interest
in video hardware (VCRs, monitors, cameras and accessories) than in Patient Education Programs. Upon this realization, he began to seek-out suppliers for this type of equipment, hoping to tap into a previously unidentified market.
Through this search, Bill discovered NZ Video, a Panasonic Professional Dealer located in Sikeston, MO, who agreed to sell Modern equipment at a resale price. This partnership allowed Bill to pursue the ever-growing requests for video hardware from these hospitals and medical centers. Slowly broadcast video business grew. In 1980, Panasonic contacted Don to partner with the Company, making Modern a direct Panasonic Professional Dealer.
Video Decks
Men shaking hands
By 1983, Modern Communications had outgrown their office in Crestwood and moved to a larger facility in Fenton. The Company now employed four people and had numerous lines of equipment to offer their clientele. In addition, the new headquarters allowed the Company to establish an in-house service center, giving Modern the capability to repair and service equipment internally.
Standing in front of sign
Modern Communications Sign
Over the next ten years, Modern Communications continued to thrive, and by 1993, the Company had outgrown their 2,500 square foot office. That spring, Don and Bill broke ground at the site of the current office, just a half mile away. By February 1994, Modern Communications, Inc. officially had a new 12,500 square foot headquarters and warehouse, providing the needed space to continue growing the business.
© Copyright 2019 Modern Communications
1231 Horan Drive, Fenton, Missouri 63026