Bifurcations of traveling wave solutions for a class of the generalized Benjamin-Bona-Mahony equation

Xiaoshan Zhao, Wei Xu, Shuang Li, Jianwei Shen

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

Abstract

By using the theory of bifurcations of dynamical systems to a class of the generalized Benjamin-Bona-Mahony (GBBM) equation, the existence of solitary wave solutions and uncountably infinite, many smooth and non-smooth periodic wave solutions are obtained. It can be shown that the existence of singular curves in a traveling wave system is the reason why smooth waves converge to cusp waves, finally. When parameters are varied, under different parametric conditions, various sufficient conditions to guarantee the existence of the above solutions are given.

Original languageEnglish
Pages (from-to)1760-1774
Number of pages15
JournalApplied Mathematics and Computation
Volume175
Issue number2
DOIs
StatePublished - 15 Apr 2006

Keywords

  • Bifurcation theory
  • Cusp wave
  • Generalized Benjamin-Bona-Mahony equation
  • Periodic wave
  • Smoothness of waves
  • Solitary wave

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