Explicit symplectic schemes for investigating the evolution of vortices in a rotating Bose–Einstein Condensate Original Research Article

The aim of this paper is to investigate vortex solutions of the Gross–Pitaevskii equation and their evolution in real time. We construct a kind of explicit symplectic leap-frog scheme. They are of arbitrary order both in time and space. First, we look for steady state solution of the imaginary time G-P equation. Then for the Bose–Einstein Condensate placed in a rotating trap and confined in the z-axis, we numerically study the cases of vorticesʹs birth and how they evolve in real time starting with the solution in imaginary time as initial value.