Peakon solutions and analytical properties for the Camassa–Holm-type equations with quadratic nonlinearities

Authors

• Yonghong Chen, The University of Texas Rio Grande Valley
• Zhijun Qiao, The University of Texas Rio Grande ValleyFollow
• Mingxuan Zhu, Qufu Normal University

Document Type

Article

Publication Date

11-15-2026

Abstract

In this paper, we derive the multi-peakon dynamical system of a class of Camassa-Holm-type equations with quadratic nonlinearities. We also consider the analytical properties for the Cauchy problem. Firstly, we establish local well-posedness of solutions in Besov spaces and then provide the blow-up criteria. Subsequently, we impose appropriate sufficient conditions on the initial data to guarantee that the corresponding solution either exists globally or blows up in a finite time. Finally, we prove the ill-posedness in the Besov space B2,∞^3/2 by utilizing the non-traveling wave solutions.

Recommended Citation

Chen, Yonghong, Zhijun Qiao, and Mingxuan Zhu. “Peakon Solutions and Analytical Properties for the Camassa–Holm-Type Equations with Quadratic Nonlinearities.” Journal of Differential Equations 481 (November 2026): 114708. https://doi.org/10.1016/j.jde.2026.114708.

Publication Title

Journal of Differential Equations

DOI

10.1016/j.jde.2026.114708