A split-step Fourier pseudo-spectral method for solving the space fractional coupled nonlinear Schrödinger equations

In this paper, we propose a split-step Fourier pseudo-spectral method for solving the space fractional coupled nonlinear Schrödinger (CNLS) equations. The space fractional CNLS equations can be split into two subproblems such that one of them is linear. The solution of the nonlinear subproblem is computed exactly. The Riesz space fractional derivative is approximated by a Fourier pseudo-spectral method. The unconditional stability, convergence, discrete charge and multi-symplectic preserving properties for the proposed method are investigated. Then, the proposed method is extended for solving the two-dimensional problem. Finally, some numerical experiments are performed to confirm our theoretical analysis and illustrate the efficiency of the proposed scheme.