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

Jianwei Shen, Wei Xu, Youming Lei

科研成果: 期刊稿件文章同行评审

14 引用 (Scopus)

摘要

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.

源语言英语
页(从-至)117-130
页数14
期刊Chaos, Solitons and Fractals
23
1
DOI
出版状态已出版 - 1月 2005

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