Completing the Study of Traveling Wave Solutions for Three Two-Component Shallow Water Wave Models
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 | 2050036 |
Journal / Publication | International Journal of Bifurcation and Chaos |
Volume | 30 |
Issue number | 3 |
Publication status | Published - 15 Mar 2020 |
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Abstract
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
Citation Format(s)
Completing the Study of Traveling Wave Solutions for Three Two-Component Shallow Water Wave Models. / Li, Jibin; Chen, Guanrong; Song, Jie.
In: International Journal of Bifurcation and Chaos, Vol. 30, No. 3, 2050036, 15.03.2020.Research output: Journal Publications and Reviews (RGC: 21, 22, 62) › 21_Publication in refereed journal › peer-review