Work

On the Periodic Cauchy Problem for the μ‐Modified Camassa‐Holm‐Novikov Type Equation

Year: 2026

Type: article

Abstract: ABSTRACT This paper delves into the intricate periodic Cauchy problem associated with the ‐modified Camassa‐Holm‐Novikov equation. We first rigorously demonstrate that the occurrence of blow‐up phenomena in this equation is exclusively manifested through the formation of breaking waves and elucidate a comprehensive wave‐breaking mechanism of the solutions under certain initial data conditions. Subsequently, the existence of peaked travelling wave solutions is established, thereby enriching the understanding of the dynamical behavior of this remarkable equation. Finally, it is shown that the data‐to‐solution map is Hölder continuous in the , with .

Source: Mathematical Methods in the Applied Sciences

DOI: 10.1002/mma.70953

Authors: Li Yang, Hongli Sun, Shanshan Zheng

Institutions: Chongqing University of Science and Technology, Nanning Normal University

Language: English

Topic: Nonlinear Waves and Solitons

Subfield: Statistical and Nonlinear Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: bronze

Funders: Chongqing University, Natural Science Foundation of Chongqing, Chongqing Municipal Education Commission, Chongqing University of Science and Technology