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 journal › peer-review
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Detail(s)
Original language | English |
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Article number | 1950153 |
Journal / Publication | International Journal of Bifurcation and Chaos |
Volume | 29 |
Issue number | 12 |
Publication status | Published - Nov 2019 |
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Abstract
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
Citation Format(s)
Exact Traveling Wave Solutions and Bifurcations of Classical and Modified Serre Shallow Water Wave Equations. / Li, Jibin; Chen, Guanrong; Song, Jie.
In: International Journal of Bifurcation and Chaos, Vol. 29, No. 12, 1950153, 11.2019.Research output: Journal Publications and Reviews (RGC: 21, 22, 62) › 21_Publication in refereed journal › peer-review