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Multi-symplectic method for generalized Boussinesq equation

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Abstract

The generalized Boussinesq equation that represents a group of important nonlinear equations possesses many interesting properties. Multi-symplectic formulations of the generalized Boussinesq equation in the Hamilton space are introduced in this paper. And then an implicit multi-symplectic scheme equivalent to the multi-symplectic Box scheme is constructed to solve the partial differential equations (PDEs) derived from the generalized Boussinesq equation. Finally, the numerical experiments on the soliton solutions of the generalized Boussinesq equation are reported. The results show that the multi-symplectic method is an efficient algorithm with excellent long-time numerical behaviors for nonlinear partial differential equations.

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Authors and Affiliations

  1. School of Mechanics, Civil Engineering and Architecture, Northwestern Polytechnical University, Xi’an, 710072, P. R. China

    Wei-peng Hu  (胡伟鹏) & Zi-chen Deng  (邓子辰)

  2. State Key Laboratory of Structural Analysis of Industrial Equipment, Dalian University of Technology, Dalian, 116023, Liaoning Province, P. R. China

    Zi-chen Deng  (邓子辰)

Authors
  1. Wei-peng Hu  (胡伟鹏)
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  2. Zi-chen Deng  (邓子辰)
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Correspondence to Zi-chen Deng  (邓子辰).

Additional information

Communicated by YUE Zhu-feng

Project supported by the National Natural Science Foundation of China (Nos. 10572119, 10772147, 10632030), the Doctoral Program Foundation of Education Ministry of China (No. 20070699028), the Natural Science Foundation of Shaanxi Province of China (No. 2006A07), and the Open Foundation of State Key Laboratory of Structural Analysis of Industrial Equipment, Dalian University of Technology.

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Hu, Wp., Deng, Zc. Multi-symplectic method for generalized Boussinesq equation. Appl. Math. Mech.-Engl. Ed. 29, 927–932 (2008). https://doi.org/10.1007/s10483-008-0711-3

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  • DOI: https://doi.org/10.1007/s10483-008-0711-3

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