Camassa-Holm Type Equations and Multi-Peakon Solutions

Author

Yonghong Chen, The University of Texas Rio Grande Valley

Date of Award

5-1-2025

Document Type

Thesis

Degree Name

Master of Science (MS)

Department

Mathematics

First Advisor

Zhijun Qiao

Second Advisor

Dambaru Bhatta

Third Advisor

Vesselin Vatchev

Abstract

This thesis investigates the multi-peakon solutions of a class of Camassa-Holm type equations with quadratic nonlinearities, specifically focusing on the differential equation mt +θmu+ amxu+bmux = 0, where m = u−uxx, and θ, a, b are arbitrary constants. We derive the nonlocal form of the equation and explore its peakon dynamics, including the well-known Camassa–Holm, Degasperis–Procesi, and Holm–Staley b-family equations. By employing a practical computational approach, we analyze the N-peakon solutions and present the corresponding dynamical systems, particularly focusing on the two-peakon case. The results will provide new insights into the integrability and peakon-interactional dynamics of these nonlinear partial differential equations with potential applications in mathematical physics and fluid dynamics.

Comments

Copyright 2025 Yonghong Chen. https://proquest.com/docview/3240867232

Recommended Citation

Chen, Y. (2025). Camassa-Holm Type Equations and Multi-Peakon Solutions [Master's thesis, The University of Texas Rio Grande Valley]. ScholarWorks @ UTRGV. https://scholarworks.utrgv.edu/etd/1722