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.
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)
