Explicit compacton and generalized kink wave solutions for a CH-DP equation

Shaoyong Li; Shangjiu Wang; Yin Li; Keqiang Li; Shaoyong Li; Shangjiu Wang; Yin Li; Keqiang Li

doi:10.3934/era.2026203

Electronic Research Archive

2026, Volume 34, Issue 7: 4611-4625. doi: 10.3934/era.2026203

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Research article

Explicit compacton and generalized kink wave solutions for a CH-DP equation

1.
School of Mathematics and Statistics, Shaoguan University, Shaoguan 512005, China
2.
School of Artificial Intelligence, Ningbo University of Finance and Economics, Ningbo 315175, China

Received: 27 January 2026 Revised: 17 May 2026 Accepted: 22 May 2026 Published: 29 May 2026

This study aimed to investigate the traveling solutions of the Camassa-Holm and Degasperis-Procesi (CH-DP) equation. By using the qualitative theory of dynamical systems and integrating along special phase orbits, we present exact explicit expressions of compacton and generalized kink wave solutions to the CH-DP equation. Our results will enrich the previous literature and help to understand the propagation of nonlinear waves.
- CH-DP equation,
- compacton,
- generalized kink,
- exact explicit expression
Citation: Shaoyong Li, Shangjiu Wang, Yin Li, Keqiang Li. Explicit compacton and generalized kink wave solutions for a CH-DP equation[J]. Electronic Research Archive, 2026, 34(7): 4611-4625. doi: 10.3934/era.2026203

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Abstract

This study aimed to investigate the traveling solutions of the Camassa-Holm and Degasperis-Procesi (CH-DP) equation. By using the qualitative theory of dynamical systems and integrating along special phase orbits, we present exact explicit expressions of compacton and generalized kink wave solutions to the CH-DP equation. Our results will enrich the previous literature and help to understand the propagation of nonlinear waves.

References

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