Solitons, peakons and periodic cusp wave solutions for the Fornberg–Whitham equation

In this paper, we employ the bifurcation method to dynamical systems to investigate the exact travelling wave solutions for the Fornberg–Whitham equation u t − u x x t + u x + u u x = u u x x x + 3 u x u x x . The implicit expression for solitons is given. The explicit expressions for peakons and pe...

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Bibliographic Details
Published in:Nonlinear analysis: real world applications 2010-02, Vol.11 (1), p.356-363
Main Authors: Zhou, Jiangbo, Tian, Lixin
Format: Article
Language:English
Subjects:
Bifurcations
Cusps
Dynamical systems
Fornberg–Whitham equation
Mathematical analysis
Nonlinearity
Peakon
Periodic cusp wave solution
Soliton
Solitons
Traveling waves
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Summary:In this paper, we employ the bifurcation method to dynamical systems to investigate the exact travelling wave solutions for the Fornberg–Whitham equation u t − u x x t + u x + u u x = u u x x x + 3 u x u x x . The implicit expression for solitons is given. The explicit expressions for peakons and periodic cusp wave solutions are also obtained. Further, we show that the limits of soliton solutions and periodic cusp wave solutions are peakons.
ISSN:1468-1218
1878-5719
DOI:10.1016/j.nonrwa.2008.11.014