Stability of 2-soliton solutions for the modified Camassa-Holm equation with cubic nonlinearity
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _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 |