Completing the Study of Traveling Wave Solutions for Three Two-Component Shallow Water Wave Models

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Original languageEnglish
Article number2050036
Journal / PublicationInternational Journal of Bifurcation and Chaos
Issue number3
Publication statusPublished - 15 Mar 2020


For three two-component shallow water wave models, from the approach of dynamical systems and the singular traveling wave theory developed in [Li & Chen, 2007], under different parameter conditions, all possible bounded solutions (solitary wave solutions, pseudo-peakons, periodic peakons, as well as smooth periodic wave solutions) are derived. More than 19 explicit exact parametric representations are obtained. Of more interest is that, for the integrable two-component generalization of the Camassa-Holm equation, it is found that its u-traveling wave system has a family of pseudo-peakon wave solutions. In addition, its h-traveling wave system has two families of uncountably infinitely many solitary wave solutions. The new results complete a recent study by Dutykh and Ionescu-Kruse [2016].

Research Area(s)

  • bifurcation, periodic peakon, periodic wave solution, pseudo-peakon, shallow water wave model, Solitary wave solution