Journal of South China University of Technology (Natural Science Edition) ›› 2007, Vol. 35 ›› Issue (8): 118-122.

• Mathematical Sciences • Previous Articles     Next Articles

Nonexistence of Solitary Peakon Solution to a Generalized Boussinesq Equation

Zhang Ben-gong  Liu Zheng-rong   

  1. School of Mathematical Science , South China Univ. of Tech. , Guangzhou 510640 , Guangdong , China
  • Received:2006-11-29 Online:2007-08-25 Published:2007-08-25
  • Contact: 张本龚(1979-) ，男，博士生，主要从事微分方程及动力系统研究. E-mail:benyan1219@126.com
  • About author:张本龚(1979-) ，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)

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Abstract:

In this paper , the qualitative theory of differential equations and the bifurcation method of dynamical systems are used to investigate the existence of the solitary peakon solution to a generalized Boussinesq equation. In the investigation , the bifurcation phase portraits of the corresponding traveling wave system are given , which are then adopted to prove the nonexistence of the solitary peakon solution to the equation.

Key words: generalized Boussinesq equation, solitarγwave, peakon solution, bifurcation phase portrait