Travelling wave solutions for a class of the generalized Benjamin-Bona-Mahoney equations

Xiaoshan Zhao; Wei Xu

doi:10.1016/j.amc.2007.03.024

Travelling wave solutions for a class of the generalized Benjamin-Bona-Mahoney equations

Xiaoshan Zhao, Wei Xu

School of Mathematics and Statistics

Northwestern Polytechnical University Xian

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

17 Scopus citations

Abstract

In this paper, a class of the generalized Benjamin-Bona-Mahony (GBBM) equations with negative exponents are investigated by using the theory of bifurcations of dynamical systems. As a result, the dynamical behavior of different physical structure: solitary patterns, solitons, perodic, kink and anti-kink wave solutions are obtained. When parameters are varied, under different parametric conditions, various sufficient conditions to guarantee the existence of the above solutions are given and some exact solutions are shown.

Original language	English
Pages (from-to)	507-519
Number of pages	13
Journal	Applied Mathematics and Computation
Volume	192
Issue number	2
DOIs	https://doi.org/10.1016/j.amc.2007.03.024
State	Published - 15 Sep 2007

Keywords

Bifurcation theory
Kink and anti-kink wave
Periodic wave
Solitary wave
The generalized Benjamin-Bona-Mahony equation

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10.1016/j.amc.2007.03.024

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abstract = "In this paper, a class of the generalized Benjamin-Bona-Mahony (GBBM) equations with negative exponents are investigated by using the theory of bifurcations of dynamical systems. As a result, the dynamical behavior of different physical structure: solitary patterns, solitons, perodic, kink and anti-kink wave solutions are obtained. When parameters are varied, under different parametric conditions, various sufficient conditions to guarantee the existence of the above solutions are given and some exact solutions are shown.",

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AU - Xu, Wei

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AB - In this paper, a class of the generalized Benjamin-Bona-Mahony (GBBM) equations with negative exponents are investigated by using the theory of bifurcations of dynamical systems. As a result, the dynamical behavior of different physical structure: solitary patterns, solitons, perodic, kink and anti-kink wave solutions are obtained. When parameters are varied, under different parametric conditions, various sufficient conditions to guarantee the existence of the above solutions are given and some exact solutions are shown.

KW - Bifurcation theory

KW - Kink and anti-kink wave

KW - Periodic wave

KW - Solitary wave

KW - The generalized Benjamin-Bona-Mahony equation

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SN - 0096-3003

VL - 192

SP - 507

EP - 519

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

IS - 2

ER -

Travelling wave solutions for a class of the generalized Benjamin-Bona-Mahoney equations

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Keywords

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