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2013 The Traveling Wave Solutions and Their Bifurcations for the BBM-Like B(m,n) Equations
Shaoyong Li, Zhengrong Liu
J. Appl. Math. 2013: 1-17 (2013). DOI: 10.1155/2013/490341

Abstract

We investigate the traveling wave solutions and their bifurcations for the BBM-like B(m,n) equations ut+αux+β(um)xγ(un)xxt=0 by using bifurcation method and numerical simulation approach of dynamical systems. Firstly, for BBM-like B(3,2) equation, we obtain some precise expressions of traveling wave solutions, which include periodic blow-up and periodic wave solution, peakon and periodic peakon wave solution, and solitary wave and blow-up solution. Furthermore, we reveal the relationships among these solutions theoretically. Secondly, for BBM-like B(4,2) equation, we construct two periodic wave solutions and two blow-up solutions. In order to confirm the correctness of these solutions, we also check them by software Mathematica.

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Shaoyong Li. Zhengrong Liu. "The Traveling Wave Solutions and Their Bifurcations for the BBM-Like B(m,n) Equations." J. Appl. Math. 2013 1 - 17, 2013. https://doi.org/10.1155/2013/490341

Information

Published: 2013
First available in Project Euclid: 14 March 2014

MathSciNet: MR3092002
Digital Object Identifier: 10.1155/2013/490341

Rights: Copyright © 2013 Hindawi

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