A Symplectic Scheme of Gross-Pitaevskii Equation

For a Bose-Einstein Condensate placed in a rotating trap and confined in the z axis, a kind of symplectic difference schemes was constructed, which is second order in time and arbitrary order in space to investigate the evolution of vortices of BEC in this paper. First, we look for a steady state solution of the imaginary time G-P equation. Then, we numerically study the vortices's development in real time, starting with the solution in imaginary time as initial value.