Time-splitting Galerkin method for spin–orbit-coupled Bose–Einstein condensates

Abstract In this paper, we develop a time-splitting method to investigate the evolution of the spin–orbit-coupled Bose–Einstein condensates. The fully discrete scheme is constructed by combining the second-order time-splitting method for temporal discretization and the framework of Galerkin finite element method for spatial discretization. Ample numerical simulations are performed to validate the features of the designed numerical method, including the optimal order of error norms, the conservation law and the center-of-mass. Moreover, the interaction of waves with typical trapping potentials in two and three dimensions is numerically simulated.