Journal of South China University of Technology (Natural Science Edition) ›› 2008, Vol. 36 ›› Issue (8): 136-139.

• Mathematics • Previous Articles     Next Articles

Peaked Solitary Wave Solution to Generalized CH-DP Equation

Ouyang Zheng-yong  Liu Zheng-rong   

  1. School of Mathematical Science, South China University of Technology, Guangzhou 510640, Guangdong, China
  • Received:2007-07-05 Revised:2007-09-30 Online:2008-08-25 Published:2008-08-25
  • Contact: 欧阳正勇（1978-），男，博士生，主要从事微分方程及动力系统研究． E-mail:oyzy1128@126．com
  • About author:欧阳正勇（1978-），男，博士生，主要从事微分方程及动力系统研究．
  • Supported by:

    国家自然科学基金资助项目（10571062）;广东省自然科学基金资助项目（07006552）

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Abstract:

This paper investigates the peaked solitary wave solutions to the generalized forms of the Camassa-Holm equation and the Degasperis-Processi equation. By means of the qualitative theory of differential equations and the bifurcation method of dynamic systems, the existence of the peaked solitary wave solutions is proved, and the ex- plicit expressions of the peaked and the smooth solitary wave solutions are respectively given. Moreover, some resuits in the literature are extended and a conjecture is clarified.

Key words: generalized CH-DP equation, bifurcation method, bifurcation phase portrait, peaked solitary wave solution