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 ...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.展开更多
基金Supported by the National Natural Science Foundation of China under Grant Nos 11075030,11105065,11275041the National Basic Research Program of China under Grant Nos 2008CB717801,2008CB787103,2009GB105004,2010GB106002the Fundamental Research Funds for the Central Universities of China under Grant Nos DUT12ZD(G)01,DUT12ZD201.
文摘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.
