A time-splitting spectral method for coupled Gross–Pitaevskii equations with applications to rotating Bose–Einstein condensates

We propose a time-splitting spectral method for the coupled Gross–Pitaevskii equations, which describe the dynamics of rotating two-component Bose–Einstein condensates at a very low temperature. The new numerical method is explicit, unconditionally stable, time reversible, time transverse invariant, and of spectral accuracy in space and second-order accuracy in time. Moreover, it conserves the position densities in the discretized level. Numerical applications on studying the generation of topological modes and the vortex lattice dynamics for the rotating two-component Bose–Einstein condensates are presented in detail.