Smooth and non-smooth travelling waves in a nonlinearly dispersive Boussinesq equation

Jianwei Shen, Wei Xu, Youming Lei

Research output: Contribution to journalArticlepeer-review

14 Scopus citations

Abstract

The dynamical behavior and special exact solutions of nonlinear dispersive Boussinesq equation (B(m,n) equation), utt-uxx-a(u n)xx+b(um)xxxx=0, is studied by using bifurcation theory of dynamical system. As a result, all possible phase portraits in the parametric space for the travelling wave system, solitary wave, kink and anti-kink wave solutions and uncountably infinite many smooth and non-smooth periodic wave solutions are obtained. It can be shown that the existence of singular straight line in the travelling wave system is the reason why smooth waves converge to cusp waves, finally. When parameter are varied, under different parametric conditions, various sufficient conditions guarantee the existence of the above solutions are given.

Original languageEnglish
Pages (from-to)117-130
Number of pages14
JournalChaos, Solitons and Fractals
Volume23
Issue number1
DOIs
StatePublished - Jan 2005

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