A semi-explicit multi-symplectic splitting scheme for a 3-coupled nonlinear Schrödinger equation
A semi-explicit multi-symplectic splitting scheme for a 3-coupled nonlinear Schrödinger equation
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DOI：
10.1016/j.cpc.2013.12.025
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发表时间：
2014-04
期刊：
影响因子：
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通讯作者：
Xu Qian;Songhe Song;Yaming Chen
中科院分区：
文献类型：
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作者：
Xu Qian;Songhe Song;Yaming Chen
本文主要提出一种有效的半显式多辛分裂格式来求解3-耦合非线性薛定谔方程。基于其多辛形式，3-CNLS方程可以分裂为一个线性多辛子系统和一个非线性无穷维Hamilton子系统。对于线性子系统，分别采用多辛傅立叶拟谱方法和辛欧拉方法进行空间和时间离散。对于非线性子系统，采用中点辛格式。对不稳定平面波的数值实验表明了该方法在长时间数值计算中的有效性。
In this paper, we mainly propose an efficient semi-explicit multi-symplectic splitting scheme to solve a 3-coupled nonlinear Schrödinger (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.