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Bifurcations and Single Peak Solitary Wave Solutions of an Integrable Nonlinear Wave Equation

Part of: Equations of mathematical physics and other areas of application

Published online by Cambridge University Press:  19 September 2016

Wei Wang ,
Chunhai Li  and
Wenjing Zhu
Wei Wang
Affiliation:
School of Mathematics and Computing Science, Guilin University of Electronic Technology, Jinji Road No. 1, Guilin 541004, China
Chunhai Li*
Affiliation:
School of Mathematics and Computing Science, Guilin University of Electronic Technology, Jinji Road No. 1, Guilin 541004, China
Wenjing Zhu
Affiliation:
School of Mathematics and Computing Science, Guilin University of Electronic Technology, Jinji Road No. 1, Guilin 541004, China
*
*Corresponding author. Email:chunhai2001@163.com (C. H. Li)
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Abstract

Dynamical system theory is applied to the integrable nonlinear wave equation ut±(u3–u2)x+(u3)xxx=0. We obtain the single peak solitary wave solutions and compacton solutions of the equation. Regular compacton solution of the equation correspond to the case of wave speed c=0. In the case of c≠0, we find smooth soliton solutions. The influence of parameters of the traveling wave solutions is explored by using the phase portrait analytical technique. Asymptotic analysis and numerical simulations are provided for these soliton solutions of the nonlinear wave equation.

Keywords

Bifurcationsolitary wavecompaction

MSC classification

Secondary: 35Q51: Soliton-like equations 35Q53: KdV-like equations (Korteweg-de Vries)
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 8 , Issue 6 , December 2016 , pp. 1084 - 1098
Copyright
Copyright © Global-Science Press 2016 

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