Multi-symplectic wavelet splitting method for the strongly coupled Schrödinger system

doi:10.1088/1674-1056/21/12/120202

Abstract We propose a multi-symplectic wavelet splitting method to solve the strongly coupled nonlinear Schrödinger equations. Based on its multi-symplectic formulation, the strongly coupled nonlinear Schrödinger equations can be split into one linear multi-symplectic subsystem and one nonlinear infinite-dimensional Hamiltonian subsystem. For the linear subsystem, multi-symplectic wavelet collocation method and symplectic Euler method are employed in spatial and temporal discretization, respectively. For the nonlinear subsystem, the mid-point symplectic scheme is used. Numerical simulations show the effectiveness of the proposed method during long-time numerical calculation.

Keywords: multi-symplectic wavelet splitting method symplectic Euler method strongly coupled nonlinear Schrödinger equations

Received: 24 May 2012
Revised: 19 June 2012
Accepted manuscript online:

PACS:	02.30.Jr	(Partial differential equations)
	02.60.Cb	(Numerical simulation; solution of equations)
	02.70.Jn	(Collocation methods)

Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 10971226, 91130013, and 11001270), the National Basic Research Program of China (Grant No. 2009CB723802), the Research Innovation Fund of Hunan Province, China (Grant No. CX2011B011), and the Innovation Fund of National University of Defense Technology, China (Grant No. B120205).

Corresponding Authors: Qian Xu
E-mail: qianxu@nudt.edu.cn

Cite this article:

Qian Xu (钱旭), Chen Ya-Ming (陈亚铭), Gao Er (高二), Song Song-He (宋松和) Multi-symplectic wavelet splitting method for the strongly coupled Schrödinger system 2012 Chin. Phys. B 21 120202

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