New periodic exact traveling wave solutions of Camassa–Holm equation

• Published in: Partial differential equations in applied mathematics : a spin-off of Applied Mathematics Letters Vol. 6; p. 100426
• Main Author: Zhang, Guoping
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.12.2022; Elsevier
• Subjects: Camassa–Holm equation; Cuspon solution; Explicit solution; Periodic; Traveling wave solution; 34A05; 34B15; 34A34; Camassa–Holm equation; 34B40; Cuspon solution; Periodic; Explicit solution; 35C08; Traveling wave solution; 35A09; 35C07
• ISSN: 2666-8181; 2666-8181
• DOI: 10.1016/j.padiff.2022.100426

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.