A Generalized Two-Component Camassa-Holm System with Complex Nonlinear Terms and Waltzing Peakons

Authors

Xiaolin Pan
Shouming Zhou
Zhijun Qiao, The University of Texas Rio Grande ValleyFollow

Document Type

Article

Publication Date

6-18-2023

Abstract

In this paper, we deal with the Cauchy problem for a generalized two-component Camassa-Holm system with waltzing peakons and complex higher-order nonlinear terms. By the classical Friedrichs regularization method and the transport equation theory, the local well-posedness of solutions for the generalized coupled Camassa-Holm system in nonhomogeneous Besov spaces and the critical Besov space B5/22,1×B5/22,1 was obtained. Besides the propagation behaviors of compactly supported solutions, the global existence and precise blow-up mechanism for the strong solutions of this system are determined. In addition to wave breaking, the another one of the most essential property of this equation is the existence of waltzing peakons and multi-peaked solitray was also obtained.

Comments

Copyright © 2023, The Author(s)

Recommended Citation

Pan, X., Zhou, S. & Qiao, Z. A Generalized Two-Component Camassa-Holm System with Complex Nonlinear Terms and Waltzing Peakons. J Nonlinear Math Phys (2023). https://doi.org/10.1007/s44198-023-00121-9

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Publication Title

J Nonlinear Math Phys

DOI

https://doi.org/10.1007/s44198-023-00121-9