Exact Traveling Wave Solutions and Bifurcations of Classical and Modified Serre Shallow Water Wave Equations

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

5 Scopus Citations
View graph of relations


Related Research Unit(s)


Original languageEnglish
Article number1950153
Journal / PublicationInternational Journal of Bifurcation and Chaos
Issue number12
Publication statusPublished - Nov 2019


Using the dynamical systems analysis and singular traveling wave theory developed by Li and Chen [2007] to the classical and modified Serre shallow water wave equations, it is shown that, in different regions of the parameter space, all possible bounded solutions (solitary wave solutions, kink wave solutions, peakons, pseudo-peakons and periodic peakons as well as compactons) can be obtained. More than 28 explicit and exact parametric representations are precisely derived. It is demonstrated that, more interestingly, the modified Serre equation has uncountably infinitely many smooth solitary wave solutions and uncountably infinitely many pseudo-peakon solutions. Moreover, it is found that, differing from the well-known peakon solution of the Camassa-Holm equation, the modified Serre equation has four new forms of peakon solutions.

Research Area(s)

  • bifurcation, compacton, kink wave, Peakon, periodic peakon, periodic wave, pseudo-peakon, Serre equation, shallow water wave model, solitary wave