New periodic exact traveling wave solutions of Camassa–Holm equation

In Zhang et al. (2007) and Zhang (2021) we constructed all single-peak traveling wave solutions of the Camassa–Holm equation including some explicit solutions. In general it is a challenge to construct exact multi-peak traveling wave solutions. As an example a periodic traveling wave (or wavetrain),...

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Bibliographic Details
Published in:Partial differential equations in applied mathematics : a spin-off of Applied Mathematics Letters 2022-12, Vol.6, p.100426, Article 100426
Main Author: Zhang, Guoping
Format: Article
Language:English
Subjects:
Camassa–Holm equation
Cuspon solution
Explicit solution
Periodic
Traveling wave solution
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Summary:In Zhang et al. (2007) and Zhang (2021) we constructed all single-peak traveling wave solutions of the Camassa–Holm equation including some explicit solutions. In general it is a challenge to construct exact multi-peak traveling wave solutions. As an example a periodic traveling wave (or wavetrain), a special type of spatiotemporal oscillation that is a periodic function of both space and time, plays a fundamental role in many mathematical equations such as shallow water wave equations. In this paper we will construct some new exact periodic traveling wave solutions of the Camassa–Holm equation.
ISSN:2666-8181
2666-8181
DOI:10.1016/j.padiff.2022.100426