Abstract
Within the framework of the Gross–Pitaevskii model, we deduce a system of equations that describes the motion of quantized vortices in Bose–Einstein condensates. We consider a strongly anisotropic magnetic trap whose trapping potential is much higher in the direction z than in the transverse direction. Under the action of this potential, the condensate takes the form of a plane disk. The transition to the two-dimensional case enables us to apply the method of matched asymptotic expansions and obtain the equations of vortex motion in the explicit form. We take into account the rotation of the condensate as a whole and the effect of dissipative processes as a result of which the system of vortices comes to the equilibrium state. Some examples of the vortex motion are presented for different values of the external parameters.
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