The generalized peakon solution for the rotation-two-component Camassa-Holm system

Zhenwei JIANG, Man Wai YUEN, Lijun ZHANG

Research output: Contribution to journalArticlespeer-review

Abstract

This paper is concerned with the rotation-two-component Camassa-Holm (R2CH) system, which is a model for equatorial water waves under the influence of the Coriolis force. The system includes the Dullin-Gottwald-Holm equation, the standard two-component integrable Camassa-Holm (CH) system and the CH equation as special cases. We aim to explore whether the R2CH system admits some generalized peakon weak solutions in the sense of distribution. The exact weak solutions in a particular form are derived by the ansatz method and they are proven to be the generalized peakon weak solutions. These solutions may help to explain the wave-breaking phenomenon in the wave motion to some extent. The method proposed in this paper is effective, which might be applied to study other nonlinear wave equations directly and even to be extend to search for fractal solitary wave. Copyright © 2022 World Scientific Publishing Company.

Original languageEnglish
JournalInternational Journal of Modern Physics B
Early online dateSep 2022
DOIs
Publication statusE-pub ahead of print - Sep 2022

Citation

Jiang, Z., Yuen, M., & Zhang, L. (2022). The generalized peakon solution for the rotation-two-component Camassa-Holm system. International Journal of Modern Physics B. Advance online publication. doi: 10.1142/S0217979223500170

Keywords

  • The rotation-two-component Camassa–Holm system
  • Distribution theory
  • Weak solution
  • Generalized peakon solution

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