中国物理B ›› 2003, Vol. 12 ›› Issue (10): 1049-1053.doi: 10.1088/1009-1963/12/10/301

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Evolution property of soliton solutions for the Whitham－Broer－Kaup equation and variant Boussinesq equation

许友生1, 吴锋民1, 林机2   

  1. (1)Institute of Nonlinear Physics, Zhejiang Normal University, Jinhua 321004, China; (2)Institute of Nonlinear Physics, Zhejiang Normal University, Jinhua 321004, China; Department of Physics, Shanghai Jiaotong University, Shanghai 200030, China
  • 收稿日期:2003-02-17 修回日期:2003-04-21 出版日期:2003-10-16 发布日期:2005-03-16
  • 基金资助:
    Project supported by the National Outstanding Youth Foundation of China (Grant No 19925522), the National Natural Science Foundation of China (Grant No 90203001) and the Natural Science Foundation of Zhejiang Province, China (Grant No 102053).

Evolution property of soliton solutions for the Whitham－Broer－Kaup equation and variant Boussinesq equation

Lin Ji (林机)ab, Xu You-Sheng (许友生)a, Wu Feng-Min (吴锋民)a   

  1. a Institute of Nonlinear Physics, Zhejiang Normal University, Jinhua 321004, China; b Department of Physics, Shanghai Jiaotong University, Shanghai 200030, China
  • Received:2003-02-17 Revised:2003-04-21 Online:2003-10-16 Published:2005-03-16
  • Supported by:
    Project supported by the National Outstanding Youth Foundation of China (Grant No 19925522), the National Natural Science Foundation of China (Grant No 90203001) and the Natural Science Foundation of Zhejiang Province, China (Grant No 102053).

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摘要： Using the standard Painlevé analysis approach, the (1+1)-dimensional Whitham－Broer－Kaup (WBK) and variant Boussinesq equations are solved. Some significant and exact solutions are given. We investigate the behaviour of the interactions between the multi-soliton-kink-type solution for the WBK equation and the multi-solitonic solutions and find the interactions are not elastic. The fission of solutions for the WBK equation and the fusions of those for the variant Boussinesq equation may occur after their interactions.

Abstract: Using the standard Painlevé analysis approach, the (1+1)-dimensional Whitham－Broer－Kaup (WBK) and variant Boussinesq equations are solved. Some significant and exact solutions are given. We investigate the behaviour of the interactions between the multi-soliton-kink-type solution for the WBK equation and the multi-solitonic solutions and find the interactions are not elastic. The fission of solutions for the WBK equation and the fusions of those for the variant Boussinesq equation may occur after their interactions.

Key words: soliton solution, soliton fission and fusion, Painlevé analysis approach, (1+1)-dimensional partial differential equation

中图分类号:  (Partial differential equations)

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