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

In this paper, we propose a split-step Fourier pseudo-spectral method for solving the space fractional coupled nonlinear Schrodinger (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. (c) 2023 Elsevier B.V. All rights reserved.

Automated summary

In this paper, a split-step Fourier pseudo-spectral method is proposed for solving the space fractional coupled nonlinear Schrodinger equations. The method splits the equations into two subproblems, with one of them being linear. The solution for the nonlinear subproblem is computed exactly, and the Riesz space fractional derivative is approximated using a Fourier pseudo-spectral method. The stability, convergence, discrete charge, and multi-symplectic preserving properties of the proposed method are investigated, and it is extended for solving two-dimensional problems. Numerical experiments are conducted to validate the theoretical analysis and demonstrate the efficiency of the proposed scheme.