Bifurcations of traveling wave solutions for a class of the generalized Benjamin-Bona-Mahony equation

Xiaoshan Zhao; Wei Xu; Shuang Li; Jianwei Shen

doi:10.1016/j.amc.2005.09.019

Bifurcations of traveling wave solutions for a class of the generalized Benjamin-Bona-Mahony equation

Xiaoshan Zhao, Wei Xu, Shuang Li, Jianwei Shen

School of Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

Abstract

By using the theory of bifurcations of dynamical systems to a class of the generalized Benjamin-Bona-Mahony (GBBM) equation, the existence of solitary wave solutions and uncountably infinite, many smooth and non-smooth periodic wave solutions are obtained. It can be shown that the existence of singular curves in a traveling wave system is the reason why smooth waves converge to cusp waves, finally. When parameters are varied, under different parametric conditions, various sufficient conditions to guarantee the existence of the above solutions are given.

Original language	English
Pages (from-to)	1760-1774
Number of pages	15
Journal	Applied Mathematics and Computation
Volume	175
Issue number	2
DOIs	https://doi.org/10.1016/j.amc.2005.09.019
State	Published - 15 Apr 2006

Keywords

Bifurcation theory
Cusp wave
Generalized Benjamin-Bona-Mahony equation
Periodic wave
Smoothness of waves
Solitary wave

Access to Document

10.1016/j.amc.2005.09.019

Cite this

@article{b7367e7d6348440cbd391903970372e3,

title = "Bifurcations of traveling wave solutions for a class of the generalized Benjamin-Bona-Mahony equation",

abstract = "By using the theory of bifurcations of dynamical systems to a class of the generalized Benjamin-Bona-Mahony (GBBM) equation, the existence of solitary wave solutions and uncountably infinite, many smooth and non-smooth periodic wave solutions are obtained. It can be shown that the existence of singular curves in a traveling wave system is the reason why smooth waves converge to cusp waves, finally. When parameters are varied, under different parametric conditions, various sufficient conditions to guarantee the existence of the above solutions are given.",

keywords = "Bifurcation theory, Cusp wave, Generalized Benjamin-Bona-Mahony equation, Periodic wave, Smoothness of waves, Solitary wave",

author = "Xiaoshan Zhao and Wei Xu and Shuang Li and Jianwei Shen",

year = "2006",

month = apr,

day = "15",

doi = "10.1016/j.amc.2005.09.019",

language = "英语",

volume = "175",

pages = "1760--1774",

journal = "Applied Mathematics and Computation",

issn = "0096-3003",

publisher = "Elsevier Inc.",

number = "2",

}

TY - JOUR

T1 - Bifurcations of traveling wave solutions for a class of the generalized Benjamin-Bona-Mahony equation

AU - Zhao, Xiaoshan

AU - Xu, Wei

AU - Li, Shuang

AU - Shen, Jianwei

PY - 2006/4/15

Y1 - 2006/4/15

N2 - By using the theory of bifurcations of dynamical systems to a class of the generalized Benjamin-Bona-Mahony (GBBM) equation, the existence of solitary wave solutions and uncountably infinite, many smooth and non-smooth periodic wave solutions are obtained. It can be shown that the existence of singular curves in a traveling wave system is the reason why smooth waves converge to cusp waves, finally. When parameters are varied, under different parametric conditions, various sufficient conditions to guarantee the existence of the above solutions are given.

AB - By using the theory of bifurcations of dynamical systems to a class of the generalized Benjamin-Bona-Mahony (GBBM) equation, the existence of solitary wave solutions and uncountably infinite, many smooth and non-smooth periodic wave solutions are obtained. It can be shown that the existence of singular curves in a traveling wave system is the reason why smooth waves converge to cusp waves, finally. When parameters are varied, under different parametric conditions, various sufficient conditions to guarantee the existence of the above solutions are given.

KW - Bifurcation theory

KW - Cusp wave

KW - Generalized Benjamin-Bona-Mahony equation

KW - Periodic wave

KW - Smoothness of waves

KW - Solitary wave

UR - http://www.scopus.com/inward/record.url?scp=33645864037&partnerID=8YFLogxK

U2 - 10.1016/j.amc.2005.09.019

DO - 10.1016/j.amc.2005.09.019

M3 - 文章

AN - SCOPUS:33645864037

SN - 0096-3003

VL - 175

SP - 1760

EP - 1774

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

IS - 2

ER -

Bifurcations of traveling wave solutions for a class of the generalized Benjamin-Bona-Mahony equation

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this