Orbital stability of smooth solitary waves for the modified Camassa-Holm equation

IF 2.9 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena Pub Date : 2026-05-01 Epub Date: 2026-02-05 DOI:10.1016/j.physd.2026.135140

Xijun Deng , Stéphane Lafortune , Zhisu Liu

引用次数: 0

Abstract

In this paper, we explore the orbital stability of smooth solitary wave solutions to the modified Camassa-Holm equation with cubic nonlinearity. These solutions, which exist on a nonzero constant background k, are unique up to translation for each permissible value of k and wave speed. By leveraging the Hamiltonian nature of the modified Camassa-Holm equation and employing three conserved functionals-comprising an energy and two Casimirs, we establish orbital stability through an analysis of the Vakhitov-Kolokolov condition. This stability pertains to perturbations of the momentum variable in

H^{1} (R)

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修正Camassa-Holm方程光滑孤立波的轨道稳定性

本文研究了具有三次非线性的修正Camassa-Holm方程光滑孤立波解的轨道稳定性。这些解存在于一个非零的恒定背景k上，对于k和波速的每一个允许值都是唯一的。通过利用改进Camassa-Holm方程的哈密顿性质，并采用三个守恒泛函——包括一个能量和两个卡西米尔，我们通过分析Vakhitov-Kolokolov条件建立了轨道稳定性。这种稳定性与H1(R)中动量变量的扰动有关。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Physica D: Nonlinear Phenomena 物理-物理：数学物理

CiteScore

7.30

自引率

7.50%

发文量

213

审稿时长

65 days

期刊介绍： Physica D (Nonlinear Phenomena) publishes research and review articles reporting on experimental and theoretical works, techniques and ideas that advance the understanding of nonlinear phenomena. Topics encompass wave motion in physical, chemical and biological systems; physical or biological phenomena governed by nonlinear field equations, including hydrodynamics and turbulence; pattern formation and cooperative phenomena; instability, bifurcations, chaos, and space-time disorder; integrable/Hamiltonian systems; asymptotic analysis and, more generally, mathematical methods for nonlinear systems.