Q:

Can gravitational waves be emitted from single neutron stars?

I wonder whether GWs can be produced and emitted by single neutron stars, since it is known that typically they must be emitted by a binary system of them.
If so, can the source be an isolated cool neutron star or, for instance, a milisecond pulsar? I am an early learner on Neutron Star Physics, so I don't know if any neutron star itself can emit GWs. I once saw an open question (with no answer in the book) which asked if a single person would emit GWs by waving its own arms, and I couldn't help getting more confused.
I am also a bit aware with the quadrupole formula for compact objects, so I cannot see how a single star could contribute nonzero terms to it.

A:

Yes, single neutron stars can emit gravitational waves if they have sufficient asymmetries.
For some background, an object symmetric about its axis of rotation does not produce gravitational waves. A quote from Hartle's An Introduction to Einstein's General Relativity in the example "A Little Rotation" on page 497 of the textbook:

Axisymmetric rotation in general is an example of a highly symmetric motion that does not produce gravitational radiation.

For clarity, "axisymmetric" means "symmetric about an axis."
To view the details of the calculation, that section of Hartle is a good resource.
However, a rotating neutron star which does not have sufficient symmetry would emit gravitational waves. What's more, as pointed out by @Harti, pulsars must exhibit some sort of asymmetry in order to emit the radiation they do - but the question is whether these asymmetries are such that they will produce detectable gravitational waves.
As a concrete mathematical example of a neutron star that could emit gravitational waves, consider this problem written by an old professor of mine...

A neutron star of mass M and uniform mass density $\rho = 3M/4\pi\bar{R}^3$ has the shape of a slightly nonspherical ellipsoid, and rotates around its shortest $(z^\prime)$ axis with rotation period $P$. The lengths of the three principal axes $x^\prime, y^\prime, z^\prime$ (fixed in the body of the star) are in the ratios $(1+\epsilon) : 1 : (1+\epsilon)^{-1}$, where $\epsilon \ll 1$.

Express the gravitational-wave luminosity of this object $(L_{GW})$ in terms of the quantities given above.
Estimate the root-mean-square value of a component of $h_{ij}^{TT}$ of the strain at distance D from the star in terms of $L_{GW}$. (Ignore the dependence on the angle between the line of sight and the rotation axis.)
Taking $M=1.4M_\odot$, $R = 10 \,\mathrm{km}$, $P = 1 \,\mathrm{ms}$, and $D = 10 \,\mathrm{kpc}$, estimate $\epsilon$ in order that $\langle(h_{ij}^{TT})^2\rangle^{1/2} \approx 10^{-23}$, the approximate current sensitivity of LIGO.

Understanding the solution would require some decent GR knowledge, but the point here is that, in principle, a single rotating body could emit gravitational radiation.
I am not sure if the particular scenario in the above problem is realistic, but it turns out that rotating neutron stars emitting gravitational waves is a realistic thing. See this article on astrobites about hunting for gravitational waves from spinning neutron stars.
A quote from the article that reinforces the above:

However, a neutron star must exhibit certain properties for it to be
  detectable through gravitational waves. A perfectly spherically
  symmetric neutron star won’t produce continuous gravitational waves as
  it rotates – the neutron star needs to maintain a long-lasting
  asymmetry. More importantly, this asymmetric distortion cannot be
  aligned with respect to the rotation axis (non-axisymmetric).

One example they mention is if the neutron star has some mountain on its surface.
(Note however that gravitational waves from single neutron stars have not yet been detected.)

