Stability of 2-soliton solutions for the modified Camassa-Holm equation with cubic nonlinearity
Xijun Deng, Stéphane Lafortune, Zhisu Liu
Published: 2025/6/9
Abstract
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 $H^2$.