Work

Dynamics of traveling waves to a shallow-water wave equation with Marangoni effect

Year: 2025

Type: article

Abstract: This paper is concerned with the existence and asymptotic behavior of traveling waves to a class of shallow-water wave equations with Marangoni effect based on Camassa-Holm equation. First, by transforming the high-order equations into ordinary differential equations, we clarify the existence of traveling waves for unperturbed equations. Then, we prove the existence of traveling waves of the equation with Marangoni perturbation by geometric singular perturbation, invariant manifold theory, and Melnikov method. Finally, we discuss the asymptotic behavior of traveling waves to both unperturbed and perturbed equations.

Source: Discrete and Continuous Dynamical Systems - B

DOI: 10.3934/dcdsb.2025152

Authors: Jianming Chen, Xiaojie Lin, Jiang Liu, Ke Wang

Institutions: Jiangsu Normal University, Huazhong University of Science and Technology

Language: English

Topic: Nonlinear Waves and Solitons

Subfield: Statistical and Nonlinear Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: diamond

Funder: National Natural Science Foundation of China

Award: G6959484024