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

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

Chin. Phys. B ›› 2012, Vol. 21 ›› Issue (12): 120202-120202.doi: 10.1088/1674-1056/21/12/120202

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

钱旭^a, 陈亚铭^a, 高二^a, 宋松和^{a b}

a Department of Mathematics and Systems Science, College of Science, National University of Defense Technology, Changsha 410073, China;
b State Key Laboratory of High Performance Computing, National University of Defense Technology, Changsha 410073, China

收稿日期:2012-05-24 修回日期:2012-06-19 出版日期:2012-11-01 发布日期:2012-11-01
基金资助:
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).

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

Qian Xu (钱旭)^a, Chen Ya-Ming (陈亚铭)^a, Gao Er (高二)^a, Song Song-He (宋松和)^{a b}

a Department of Mathematics and Systems Science, College of Science, National University of Defense Technology, Changsha 410073, China;
b State Key Laboratory of High Performance Computing, National University of Defense Technology, Changsha 410073, China

Received:2012-05-24 Revised:2012-06-19 Online:2012-11-01 Published:2012-11-01
Contact: Qian Xu E-mail:qianxu@nudt.edu.cn
Supported by:
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).

摘要/Abstract

摘要： 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.

关键词: multi-symplectic wavelet splitting method, symplectic Euler method, strongly coupled nonlinear Schrö, dinger equations

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.

Key words: multi-symplectic wavelet splitting method, symplectic Euler method, strongly coupled nonlinear Schrödinger equations

中图分类号: (Partial differential equations)

02.30.Jr

02.60.Cb (Numerical simulation; solution of equations) 02.70.Jn (Collocation methods)

钱旭, 陈亚铭, 高二, 宋松和. Multi-symplectic wavelet splitting method for the strongly coupled Schrödinger system[J]. Chin. Phys. B, 2012, 21(12): 120202-120202.

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[J]. Chin. Phys. B, 2012, 21(12): 120202-120202.

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

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

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