Abstract
In this paper, a splitting method for solving a system of coupled stochastic nonlinear Schrödinger (CSNLS) equations is proposed. Based on its Hamiltonian structure, the CSNLS equations split into two subproblems such that one of them is linear. The solution of the nonlinear subproblem is computed exactly, and the linear subproblem is discritized through a compact method in the spatial direction and the symplectic implicit midpoint rule with respect to the time variable. Stability, discrete stochastic multi-symplectic conservation law, discrete charge and energy conservation laws for the proposed method are investigated. Numerical results are reported for various amplitudes of noise. We present the propagation and collision of solitons which are different from the deterministic case. Finally, the mean-square order of convergence of the proposed algorithm in the temporal and spatial directions for the CSNLS equations is investigated in a numerical example.
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