Dynamics of interacting two vortex N-gons in BECs

Equations governing the motion of vortex N-gons in a Bose-Einstein condensate enclosed in a harmonic trap are obtained. It is shown that these equations have two first integrals: the integral of energy and the integral of the moment. The reduction on the fixed level set of the integral of moment is carried out. The equilibrium positions of the system considered are found. Phase portraits of the system of two vortex N-gons, each of which consists of two vortices, are constructed.