中国物理B ›› 2009, Vol. 18 ›› Issue (3): 1161-1167.doi: 10.1088/1674-1056/18/3/053

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Painleve properties and exact solutions for the high-dimensional Schwartz Boussinesq equation

任博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;Abdus Salam International Centre for Theoretical Physics, Trieste 34139, Italy
  • 收稿日期:2008-07-02 修回日期:2008-08-17 出版日期:2009-03-20 发布日期:2009-03-20
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No 10575087) and the Natural Science Foundation of Zhejiang Province, China (Grant No 102053).

Painlevé properties and exact solutions for the high-dimensional Schwartz Boussinesq equation

Ren Bo(任博)a) and Lin Ji(林机)a)b)†   

  1. a Institute of Nonlinear Physics, Zhejiang Normal University, Jinhua 321004, China; b Abdus Salam International Centre for Theoretical Physics, Trieste 34139, Italy
  • Received:2008-07-02 Revised:2008-08-17 Online:2009-03-20 Published:2009-03-20
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No 10575087) and the Natural Science Foundation of Zhejiang Province, China (Grant No 102053).

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摘要： The usual (1+1)-dimensional Schwartz Boussinesq equation is extended to the (1+1)-dimensional space--time symmetric form and the general (n+1)-dimensional space--time symmetric form. These extensions are Painlevé integrable in the sense that they possess the Painlevé property. The single soliton solutions and the periodic travelling wave solutions for arbitrary dimensional space--time symmetric form are obtained by the Painlevé—B?acklund transformation.

关键词: high-dimensional integrable model, Schwartz Boussinesq equation, Painlevé integrable

Abstract: The usual (1+1)-dimensional Schwartz Boussinesq equation is extended to the (1+1)-dimensional space--time symmetric form and the general (n+1)-dimensional space--time symmetric form. These extensions are Painlevé integrable in the sense that they possess the Painlevé property. The single soliton solutions and the periodic travelling wave solutions for arbitrary dimensional space--time symmetric form are obtained by the Painlevé—Bäcklund transformation.

Key words: high-dimensional integrable model, Schwartz Boussinesq equation, Painlevé integrable

中图分类号:  (Solitons)

  • 05.45.Yv
02.30.Ik (Integrable systems) 02.30.Gp (Special functions) 02.40.-k (Geometry, differential geometry, and topology)