中国物理B ›› 2005, Vol. 14 ›› Issue (11): 2158-2163.doi: 10.1088/1009-1963/14/11/003

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A method for constructing exact solutions and　application to Benjamin Ono equation

王振1, 鲁慧芳1, 张鸿庆1, 李德生2   

  1. (1)Department of Applied Mathematics, Dalian University of Technology, Dalian 116024,China; (2)Department of Applied Mathematics, Dalian University of Technology, Dalian 116024,China;Department of Mathematics, Shenyang Normal University,Shenyang 110034, China
  • 收稿日期:2005-04-20 修回日期:2005-06-06 出版日期:2005-11-20 发布日期:2005-11-20
  • 基金资助:
    Project supported by a National Key Basic Research Project of China (Grant No 2004CB318000).

A method for constructing exact solutions and application to Benjamin Ono equation

Wang Zhen (王振)a, Li De-Sheng (李德生)ab, Lu Hui-Fang (鲁慧芳)a, Zhang Hong-Qing (张鸿庆)a   

  1. a Department of Applied Mathematics, Dalian University of Technology, Dalian 116024, China; b Department of Mathematics, Shenyang Normal University, Shenyang 110034, China
  • Received:2005-04-20 Revised:2005-06-06 Online:2005-11-20 Published:2005-11-20
  • Supported by:
    Project supported by a National Key Basic Research Project of China (Grant No 2004CB318000).

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摘要： By using an improved projective Riccati equation method, this paper obtains several types of exact travelling wave solutions to the Benjamin Ono equation which include multiple soliton solutions, periodic soliton solutions and Weierstrass function solutions. Some of them are found for the first time. The method can be applied to other nonlinear evolution equations in mathematical physics.

关键词: Benjamin Ono equation, nonlinear evolution equation, Weierstrass function solutions, exact solutions

Abstract: By using an improved projective Riccati equation method, this paper obtains several types of exact travelling wave solutions to the Benjamin Ono equation which include multiple soliton solutions, periodic soliton solutions and Weierstrass function solutions. Some of them are found for the first time. The method can be applied to other nonlinear evolution equations in mathematical physics.

Key words: Benjamin Ono equation, nonlinear evolution equation, Weierstrass function solutions, exact solutions

中图分类号:  (Solitons)

  • 05.45.Yv
02.30.-f (Function theory, analysis)