中国物理B ›› 2008, Vol. 17 ›› Issue (11): 3923-3929.doi: 10.1088/1674-1056/17/11/001

• •    下一篇

Multi-symplectic method for generalized fifth-order KdV equation

胡伟鹏1, 邓子辰2   

  1. (1)School of Mechanics, Civil Engineering and Architecture, Northwestern Polytechnical University, Xi'an 710072, China; (2)School of Mechanics, Civil Engineering and Architecture, Northwestern Polytechnical University, Xi'an 710072, China；State Key Laboratory of Structural Analysis of Industrial Equipment, Dalian University of Technology, Dalian 116023, China
  • 收稿日期:2008-02-27 修回日期:2008-03-14 出版日期:2008-11-20 发布日期:2008-11-20
  • 基金资助:
    Project 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 National Natural Science Foundation of Shaanxi Province of China (Grant No 2006A07), the Open Foundation of State Key Laboratory of Structural Analysis of Industrial Equipment.

Multi-symplectic method for generalized fifth-order KdV equation

Hu Wei-Peng (胡伟鹏)a, Deng Zi-Chen (邓子辰)ab   

  1. a School of Mechanics, Civil Engineering and Architecture, Northwestern Polytechnical University, Xi'an 710072, China; b State Key Laboratory of Structural Analysis of Industrial Equipment, Dalian University of Technology, Dalian 116023, China
  • Received:2008-02-27 Revised:2008-03-14 Online:2008-11-20 Published:2008-11-20
  • Supported by:
    Project 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 National Natural Science Foundation of Shaanxi Province of China (Grant No 2006A07), the Open Foundation of State Key Laboratory of Structural Analysis of Industrial Equipment.

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摘要： This paper considers the multi-symplectic formulations of the generalized fifth-order KdV equation in Hamiltonian space. Recurring to the midpoint rule, it presents an implicit multi-symplectic scheme with discrete multi-symplectic conservation law to solve the partial differential equations which are derived from the generalized fifth-order KdV equation numerically. The results of the numerical experiments show that this multi-symplectic algorithm is good in accuracy and its long-time numerical behaviour is also perfect.

关键词: generalized fifth-order KdV equation, multi-symplectic, travelling wave solution, conservation law

Abstract: This paper considers the multi-symplectic formulations of the generalized fifth-order KdV equation in Hamiltonian space. Recurring to the midpoint rule, it presents an implicit multi-symplectic scheme with discrete multi-symplectic conservation law to solve the partial differential equations which are derived from the generalized fifth-order KdV equation numerically. The results of the numerical experiments show that this multi-symplectic algorithm is good in accuracy and its long-time numerical behaviour is also perfect.

Key words: generalized fifth-order KdV equation, multi-symplectic, travelling wave solution, conservation law

中图分类号:  (Solitons)

  • 05.45.Yv
02.30.Jr (Partial differential equations)