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

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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 languageEnglish
Pages (from-to)1488-1503
Number of pages16
JournalCommunications in Nonlinear Science and Numerical Simulation
Volume12
Issue number8
DOIs
Publication statusPublished - 1 Dec 2007
Externally publishedYes

Keywords

  • Bifurcation theory
  • Cusp wave
  • Periodic wave
  • RLW equation
  • Solitary wave

ASJC Scopus subject areas

  • Mechanical Engineering
  • Statistical and Nonlinear Physics

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