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

数学与统计学院

Northwestern Polytechnical University Xian
TianJin University of Technology and Education

科研成果: 期刊稿件 › 文章 › 同行评审

7 引用（Scopus）

摘要

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.

源语言	英语
页（从-至）	1760-1774
页数	15
期刊	Applied Mathematics and Computation
卷	175
期	2
DOI	https://doi.org/10.1016/j.amc.2005.09.019
出版状态	已出版 - 15 4月 2006

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10.1016/j.amc.2005.09.019

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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",

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

language = "英语",

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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 - https://www.scopus.com/pages/publications/33645864037

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

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