A semi-explicit multi-symplectic splitting scheme for a 3-coupled nonlinear Schr枚dinger equation

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• 作者：Xu Qian^a ; ^{qianxu@nudt.edu.cn" class="auth_mail} ; Songhe Song^a ; ^b ; Yaming Chen^a
• 关键词：Multi-symplectic ; Splitting method ; Fourier pseudospectral method ; Symplectic Euler method ; Coupled nonlinear Schrö ; dinger equation
• 刊名：Computer Physics Communications
• 出版年：April, 2014
• 年：2014
• 卷：185
• 期：4
• 页码：1255-1264
• 全文大小：1652 K

文摘

In this paper, we mainly propose an efficient semi-explicit multi-symplectic splitting scheme to solve a 3-coupled nonlinear Schr枚dinger (3-CNLS) equation. Based on its multi-symplectic formulation, the 3-CNLS equation can be split into one linear multi-symplectic subsystem and one nonlinear infinite-dimensional Hamiltonian subsystem. For the linear subsystem, the multi-symplectic Fourier pseudospectral method and symplectic Euler method are employed in spatial and temporal discretizations, respectively. For the nonlinear subsystem, the mid-point symplectic scheme is used. Numerical experiments for the unstable plane waves show the effectiveness of the proposed method during long-time numerical calculation.