Dynamics of three vortices Bose-Einstein condensates

We consider the asymptotic motion equations of vortices for the time-dependent Gross-Pitaevskii equation with a harmonic trap potential. The asymptotic motion equations form a system of ordinary differential equations which can be regarded as a perturbation of the standard Kirchhoff problem. From the numerical simulation on the asymptotic motion equations, we observe that the bounded and collisionless trajectories of three vortices form chaotic, quasi 2- or quasi 3-periodic orbits. Furthermore, a new phenomenon of 1 : 1-topological synchronization is observed in the chaotic trajectories of two vortices. (c) 2004 WILEY-VCH Verlag GmbH & Co. KGaA. Weinheim.