Stability of 2-soliton solutions for the modified Camassa-Holm equation with cubic nonlinearity

Fuente: arXiv
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Main Authors: Deng, Xijun, Lafortune, Stéphane, Liu, Zhisu
Format: Preprint
Published: 2025
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_version_ 1866916926995824640
author Deng, Xijun
Lafortune, Stéphane
Liu, Zhisu
author_facet Deng, Xijun
Lafortune, Stéphane
Liu, Zhisu
contents In this paper, we are concerned with the stability of 2-soliton solutions on a nonzero constant background for the modified Camassa-Holm equation with cubic nonlinearity. By employing conserved quantities in terms of the momentum variable $m$, we show that the 2-soliton, when regarded as a solution to the initial-value problem for the modified Camassa-Holm equation, is nonlinearly stable to perturbations with respect to the momentum variable in the Sobolev space $H^2$.
format Preprint
id arxiv_https___arxiv_org_abs_2506_07791
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Stability of 2-soliton solutions for the modified Camassa-Holm equation with cubic nonlinearity
Deng, Xijun
Lafortune, Stéphane
Liu, Zhisu
Analysis of PDEs
Exactly Solvable and Integrable Systems
37K10, 35B35, 76B15, 35Q51, 35C08
In this paper, we are concerned with the stability of 2-soliton solutions on a nonzero constant background for the modified Camassa-Holm equation with cubic nonlinearity. By employing conserved quantities in terms of the momentum variable $m$, we show that the 2-soliton, when regarded as a solution to the initial-value problem for the modified Camassa-Holm equation, is nonlinearly stable to perturbations with respect to the momentum variable in the Sobolev space $H^2$.
title Stability of 2-soliton solutions for the modified Camassa-Holm equation with cubic nonlinearity
topic Analysis of PDEs
Exactly Solvable and Integrable Systems
37K10, 35B35, 76B15, 35Q51, 35C08
url https://arxiv.org/abs/2506.07791