中国物理B ›› 2007, Vol. 16 ›› Issue (8): 2167-2179.doi: 10.1088/1009-1963/16/8/004

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Study on an extended Boussinesq equation

陈春丽1, 李翊神2, 张近3   

  1. (1)Department of Mathematics, Shanghai Jiaotong University, Shanghai 200240, China ; (2)Department of Mathematics, University of Science and Technology of China, Hefei 230026, China; (3)SB and SEF, The University of Hong Kong,Pokfulam Road, Hong Kong, China
  • 收稿日期:2006-10-11 修回日期:2007-02-23 出版日期:2007-08-20 发布日期:2007-08-20
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No 10401022).

Study on an extended Boussinesq equation

Chen Chun-Li(陈春丽)a)†, Zhang Jin E(张近)b), and Li Yi-Shen(李翊神)c)   

  1. a Department of Mathematics, Shanghai Jiaotong University, Shanghai 200240, China ; b SB and SEF, The University of Hong Kong,Pokfulam Road, Hong Kong, China; c Department of Mathematics, University of Science and Technology of China, Hefei 230026, China
  • Received:2006-10-11 Revised:2007-02-23 Online:2007-08-20 Published:2007-08-20
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No 10401022).

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摘要： An extended Boussinesq equation that models weakly nonlinear and weakly dispersive waves on a uniform layer of water is studied in this paper. The results show that the equation is not Painlev\'e-integrable in general. Some particular exact travelling wave solutions are obtained by using a function expansion method. An approximate solitary wave solution with physical significance is obtained by using a perturbation method. We find that the extended Boussinesq equation with a depth parameter of $1/\sqrt 2$ is able to match the Laitone's (1960) second order solitary wave solution of the Euler equations.

关键词: Painlev\'e-integrability, exact soliton solutions, approximate solution

Abstract: An extended Boussinesq equation that models weakly nonlinear and weakly dispersive waves on a uniform layer of water is studied in this paper. The results show that the equation is not Painlevé-integrable in general. Some particular exact travelling wave solutions are obtained by using a function expansion method. An approximate solitary wave solution with physical significance is obtained by using a perturbation method. We find that the extended Boussinesq equation with a depth parameter of $1/\sqrt 2$ is able to match the Laitone's (1960) second order solitary wave solution of the Euler equations.

Key words: Painlevé-integrability, exact soliton solutions, approximate solution

中图分类号:  (Solitons)

  • 05.45.Yv
47.35.Fg (Solitary waves)