A New Multi-Symplectic Integration Method for the Nonlinear Schrödinger Equation
LV Zhong-Quan1,2, WANG Yu-Shun1,3, SONG Yong-Zhong1**
1Jiangsu Key Laboratory for NSLSCS School of Mathematical Science, Nanjing Normal University, Nanjing 210046 2College of Science, Nanjing Forestry University, Nanjing 210037 3Lasg, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029
We propose a new multi-symplectic integration method for the nonlinear Schrödinger equation. The new scheme is derived by concatenating spatial discretization of the multi-symplectic Fourier pseudospectral method with temporal discretization of a symplectic Euler scheme and it is semi-explicit in the sense that it does not need to solve the nonlinear algebraic equations at every time step. We verify that the multi-symplectic semi-discretization of the Schrödinger equation with periodic boundary conditions has N semi-discrete multi-symplectic conservation laws. The discretization in time of the semi-discretization leads to N full-discrete multi-symplectic conservation laws. Numerical results are presented to demonstrate the robustness and the stability.
. [J]. 中国物理快报, 2013, 30(3): 30201-030201.
LV Zhong-Quan, WANG Yu-Shun, SONG Yong-Zhong. A New Multi-Symplectic Integration Method for the Nonlinear Schrödinger Equation. Chin. Phys. Lett., 2013, 30(3): 30201-030201.