Work

A family of μ -Camassa–Holm-type equations with peaked solutions

Year: 2025

Type: article

Abstract: In this paper, we present a general family of nonlinear dispersive wave equations, which can be regarded as a nonlocal counterpart of the f g -family. We first show that the family of equations admits multi-peaked and single peaked solutions under certain conditions on two arbitrary functions. As typical subfamilies of the equations with peaked solutions, two generalized versions of the μ -Camassa–Holm and modified μ -Camassa–Holm equations are then proposed respectively, which preserve the Hamiltonian structure shared by the μ -Camassa–Holm and modified μ -Camassa–Holm equations. The peaked solutions and higher-order conserved densities are derived from these generalized equations. Furthermore, the interactions of two-peaked solutions are exhibited. It demonstrates that the higher-order nonlinearities have an impact on interactions of peaked solutions.

Source: Physica D Nonlinear Phenomena

DOI: 10.1016/j.physd.2025.134671

Authors: Hao Wang, Kexin Yan, Ying Fu

Institutions: Xi'an University of Architecture and Technology, Ningbo University, Northwest University

Language: English

Topic: Nonlinear Waves and Solitons

Subfield: Statistical and Nonlinear Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,640

Funders: National Natural Science Foundation of China, China Postdoctoral Science Foundation