Chin. Phys. B, 2012, Vol. 21(12): 120202    DOI: 10.1088/1674-1056/21/12/120202
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# Multi-symplectic wavelet splitting method for the strongly coupled Schrödinger system

Qian Xua, Chen Ya-Minga, Gao Era, Song Song-Hea 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
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      Published:  01 November 2012
 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