| Vortex in Bose-Einstein condensate (BEC) has been a hot topic since BEC was first realized in dilute atomic vapor. Unlike the method which is based on the mean-field theory in this paper we consider the dynamics of vortices in BEC under an ordinary equation. According to the equation, the motion of the vortex includes two ingredients:for the one is the effect from the harmonic potential, the other is the interaction between vortices. This paper contains of five parts. In chapter1we give a simple introduction about the vortex in BEC as well as the evolution about the study in vortex. In chapter2, besides listing a number of preknowledge, we mainly analysis the properties of the dynamics such as the conservative, integrable Hamiltonian and so on. In chapter3, we pay attention to the dynamics among the multi-vortex as the number of the vortex is five, six as well as n, respectively, analysis the stability of the equilibria and the existence of the closed period orbit around the equilibria; In the forth part we analysis the epicyclic motion of the vortex as well as its stability; Ultimately we give a summery about the main results and an outlook about the further study in the field. |
