A Numerical Treatment for the Stability of Josephson Vortices in BEC

We consider a system of a pair of quasi one dimensional BoseEinstein condensates which are coupled with each other. The waveguides of the two condensates are assumed to be parallel. The system can be characterized by two coupled nonlinear Schrodinger equations. This system admits different topological structures such as vortices. We present a numerical treatment for the stability of Josephson vortices and dark solitons in a coupled system of Bose-Einstein condensate