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A time-splitting spectral method for coupled Gross-Pitaevskii equations with applications to rotating Bose-Einstein condensates. (English) Zbl 1118.65112

Summary: 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.

MSC:

65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
35Q55 NLS equations (nonlinear Schrödinger equations)
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
82C20 Dynamic lattice systems (kinetic Ising, etc.) and systems on graphs in time-dependent statistical mechanics
82-08 Computational methods (statistical mechanics) (MSC2010)
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