Exponential time differencing schemes for the 3-coupled nonlinear fractional Schrödinger equation

Abstract

Abstract Two modified exponential time differencing schemes based on the Fourier spectral method are developed to solve the 3-coupled nonlinear fractional Schrödinger equation. We compare the stability of the schemes by plotting their stability regions. The local truncation errors of the time integrators are proved to be fourth-order. Numerical experiments illustrating the solution to the equations with various parameters and the mass conservation results of the numerical methods are carried out.

Keywords

• Space-fractional
• Nonlinear Schrödinger equations
• Exponential time differencing
• Spectral method
• Fractional Laplacian