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arXiv · 2506.07791

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

Xijun Deng·Stéphane Lafortune·Zhisu Liu
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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 $H^2$.

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Xijun Deng, Stéphane Lafortune, Zhisu Liu. 2025-06-09. Stability of 2-soliton solutions for the modified Camassa-Holm equation with cubic nonlinearity. https://arxiv.org/abs/2506.07791

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