text: As in many other systems, vortices can exist in BECs. 
  Vortices can be created, for example, by "stirring" the condensate with lasers, 
  rotating the confining trap, 
  or by rapid cooling across the phase transition. 
  The vortex created will be a quantum vortex with core shape determined by the interactions. Fluid circulation around any point is quantized due to the single-valued nature of the order BEC order parameter or wavefunction, that can be written in the form  where  and  are as in the cylindrical coordinate system, and  is the angular quantum number (a.k.a. the "charge" of the vortex). Since the energy of a vortex is proportional to the square of its angular momentum, in trivial topology only  vortices can exist in the steady state; Higher-charge vortices will have a tendency to split into  vortices, if allowed by the topology of the geometry.
  An axially symmetric (for instance, harmonic) confining potential is commonly used for the study of vortices in BEC. To determine , the energy of  must be minimized, according to the constraint . This is usually done computationally, however, in a uniform medium, the following analytic form demonstrates the correct behavior, and is a good approximation:
  Here,  is the density far from the vortex and , where  is the healing length of the condensate.
  A singly charged vortex () is in the ground state, with its energy  given by
  where  is the farthest distance from the vortices considered.(To obtain an energy which is well defined it is necessary to include this boundary .)
  For multiply charged vortices () the energy is approximated by
  which is greater than that of  singly charged vortices, indicating that these multiply charged vortices are unstable to decay. Research has, however, indicated they are metastable states, so may have relatively long lifetimes.
  Closely related to the creation of vortices in BECs is the generation of so-called dark solitons in one-dimensional BECs. These topological objects feature a phase gradient across their nodal plane, which stabilizes their shape even in propagation and interaction. Although solitons carry no charge and are thus prone to decay, relatively long-lived dark solitons have been produced and studied extensively.