Understanding Peakons, Periodic Peakons and Compactons via a Shallow Water Wave Equation

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Original languageEnglish
Article number1650207
Journal / PublicationInternational Journal of Bifurcation and Chaos
Issue number12
Publication statusPublished - Nov 2016


In this paper, a shallow water wave model is used to introduce the concepts of peakon, periodic peakon and compacton. Traveling wave solutions of the shallow water equation are presented. The corresponding traveling wave system is a singular planar dynamical system with one singular straight line. By using the method of dynamical systems, bifurcation diagrams and explicit exact parametric representations of the solutions are given, including solitary wave solution, periodic wave solution, peakon solution, periodic peakon solution and compacton solution under different parameter conditions.

Research Area(s)

  • compacton solution, peakon solution, periodic peakon solution, periodic wave solution, Solitary wave solution