The complex multi-symplectic scheme for the generalized sinh-Gordon equation  

作　　者：HU WeiPeng DENG ZiChen HAN SongMei FAN Wei 

机构地区：[1]School of Mechanics,Civil Engineering and Architecture,Northwestern Polytechnical University,Shaanxi 710072,China [2]School of Power and Energy,Northwestern Polytechnical University,Shaanxi 710072,China [3]State Key Laboratory of Structural Analysis of Industrial Equipment,Dalian University of Technology,Dalian 116023,China

出　　处：《Science China(Physics,Mechanics & Astronomy)》2009年第10期1618-1623,共6页中国科学：物理学、力学、天文学（英文版）

基　　金：Supported by the National Natural Science Foundation of China (Grant Nos.10572119,10772147,and 10632030);the Doctoral Program Foundation of Education Ministry of China (Grant No.20070699028);the China Postdoctoral Science Foundation (Grant No. 20090450170);the National Natural Science Foundation of Shaanxi Province of China (Grant No.2006A07);the NPU Foundation for Fundamental Research and the Open Foundation of State Key Laboratory of Structural Analysis of Industrial Equipment (Grant No.GZ0802)

摘　　要：In this paper,the complex multi-symplectic method and the implementation of the generalized sinhGordon equation are investigated in detail.The multi-symplectic formulations of the generalized sinh-Gordon equation in Hamiltonian space are presented firstly.The complex method is introduced and a complex semi-implicit scheme with several discrete conservation laws(including a multi-symplectic conservation law(CLS),a local energy conservation law(ECL) as well as a local momentum conservation law(MCL)) is constructed to solve the partial differential equations(PDEs) that are derived from the generalized sinh-Gordon equation numerically.The results of the numerical experiments show that the multi-symplectic scheme has excellent long-time numerical behavior and high accuracy.In this paper, the complex multi-symplectic method and the implementation of the generalized sinh- Gordon equation are investigated in detail. The multi-symplectic formulations of the generalized sinh-Gordon equation in Hamiltonian space are presented firstly. The complex method is introduced and a complex semi-implicit scheme with several discrete conservation laws (including a multi-symplectic conservation law (CLS), a local energy conservation law (ECL) as well as a local momentum conservation law (MCL)) is constructed to solve the partial differential equations (PDEs) that are derived from the generalized sinh- Gordon equation numerically. The results of the numerical experiments show that the multi-symplectic scheme has excellent long-time numerical behavior and high accuracy.

关 键 词：GENERALIZED sinh-Gordon EQUATION MULTI-SYMPLECTIC COMPLEX method RUNGE-KUTTA methods 

分 类 号：O175[理学—数学]