Explicit high accuracy energy-preserving Lie-group sine pseudo-spectral methods for the coupled nonlinear Schrödinger equation

Abstract

The newly developed generalized scalar auxiliary variable (GSAV) approaches are very popular methods that can be applied to construct high-accuracy energy-preserving schemes for conservative systems. However, these proposed high-order schemes are fully-implicit and have the disadvantages of huge calculating quantities and long computing time for solving nonlinear systems. Therefore, we develop in this paper explicit energy-preserving schemes to deal with the coupled nonlinear Schrödinger equation by combining the Lie-group method and GSAV approaches. The given schemes are very efficient, have high accuracy, and can inherit the modified energy of the system. Ample numerical results are presented to confirm the developed schemes' efficiency, accuracy, and conservation.