Efficient Conformal Multi‐Symplectic Structure‐Preserving Method for Two‐Dimensional Damped Nonlinear Schrödinger Equation

ABSTRACT

In this paper, an efficient conformal multi‐symplectic structure‐preserving method is proposed for two‐dimensional damped nonlinear Schrödinger equation. The method decomposes the original equation into several tractable one‐dimensional subproblems by the splitting method, and then solves them separately and alternatively, and combines the resulting schemes by an appropriate method lastly. Moreover, the spatial derivatives are discretized with a high‐order compact scheme which uses fewer grid nodes to achieve higher accuracy and improve the computational efficiency. Based on this framework, an efficient conformal multi‐symplectic algorithm is developed for the equation. Some numerical experiments are reported to verify the effectiveness of the new scheme.