Bifurcation of travelling wave solutions in a nonlinear variant of the RLW equation

Yijun Lou

doi:10.1016/j.cnsns.2006.03.010

Bifurcation of travelling wave solutions in a nonlinear variant of the RLW equation

Yijun Lou

Research output: Journal article publication › Journal article › Academic research › peer-review

4 Citations (Scopus)

Abstract

By using the method of planar dynamical systems to a nonlinear variant of the regularized long-wave equation (RLW equation in short), the existence of smooth and non-smooth solitary wave (so called peakon and valleyon) and infinite many periodic wave solutions is shown. Under different regions of parametric spaces, various sufficient conditions to guarantee the existence of above solutions are given. The formulas to compute the travelling waves are also educed. We notice that some results in [Wazwaz AM. Analytic study on nonlinear variants of the RLW and the PHI-four equations. Commun Nonlinear Sci Numer Simul, in press, doi:10.1016/j.cnsns.2005.03.001] are incorrect.

Original language	English
Pages (from-to)	1488-1503
Number of pages	16
Journal	Communications in Nonlinear Science and Numerical Simulation
Volume	12
Issue number	8
DOIs	https://doi.org/10.1016/j.cnsns.2006.03.010
Publication status	Published - 1 Dec 2007
Externally published	Yes

Keywords

Bifurcation theory
Cusp wave
Periodic wave
RLW equation
Solitary wave

ASJC Scopus subject areas

Mechanical Engineering
Statistical and Nonlinear Physics

More information

10.1016/j.cnsns.2006.03.010

Cite this

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title = "Bifurcation of travelling wave solutions in a nonlinear variant of the RLW equation",

abstract = "By using the method of planar dynamical systems to a nonlinear variant of the regularized long-wave equation (RLW equation in short), the existence of smooth and non-smooth solitary wave (so called peakon and valleyon) and infinite many periodic wave solutions is shown. Under different regions of parametric spaces, various sufficient conditions to guarantee the existence of above solutions are given. The formulas to compute the travelling waves are also educed. We notice that some results in [Wazwaz AM. Analytic study on nonlinear variants of the RLW and the PHI-four equations. Commun Nonlinear Sci Numer Simul, in press, doi:10.1016/j.cnsns.2005.03.001] are incorrect.",

keywords = "Bifurcation theory, Cusp wave, Periodic wave, RLW equation, Solitary wave",

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year = "2007",

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doi = "10.1016/j.cnsns.2006.03.010",

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T1 - Bifurcation of travelling wave solutions in a nonlinear variant of the RLW equation

AU - Lou, Yijun

PY - 2007/12/1

Y1 - 2007/12/1

N2 - By using the method of planar dynamical systems to a nonlinear variant of the regularized long-wave equation (RLW equation in short), the existence of smooth and non-smooth solitary wave (so called peakon and valleyon) and infinite many periodic wave solutions is shown. Under different regions of parametric spaces, various sufficient conditions to guarantee the existence of above solutions are given. The formulas to compute the travelling waves are also educed. We notice that some results in [Wazwaz AM. Analytic study on nonlinear variants of the RLW and the PHI-four equations. Commun Nonlinear Sci Numer Simul, in press, doi:10.1016/j.cnsns.2005.03.001] are incorrect.

AB - By using the method of planar dynamical systems to a nonlinear variant of the regularized long-wave equation (RLW equation in short), the existence of smooth and non-smooth solitary wave (so called peakon and valleyon) and infinite many periodic wave solutions is shown. Under different regions of parametric spaces, various sufficient conditions to guarantee the existence of above solutions are given. The formulas to compute the travelling waves are also educed. We notice that some results in [Wazwaz AM. Analytic study on nonlinear variants of the RLW and the PHI-four equations. Commun Nonlinear Sci Numer Simul, in press, doi:10.1016/j.cnsns.2005.03.001] are incorrect.

KW - Bifurcation theory

KW - Cusp wave

KW - Periodic wave

KW - RLW equation

KW - Solitary wave

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DO - 10.1016/j.cnsns.2006.03.010

M3 - Journal article

SN - 1007-5704

VL - 12

SP - 1488

EP - 1503

JO - Communications in Nonlinear Science and Numerical Simulation

JF - Communications in Nonlinear Science and Numerical Simulation

IS - 8

ER -

Bifurcation of travelling wave solutions in a nonlinear variant of the RLW equation

Abstract

Keywords

ASJC Scopus subject areas

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