Asymptotic Stability of multi-solitons for $1$d Supercritical NLS
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_ | 1866918197688532992 |
|---|---|
| author | Chen, Gong Moutinho, Abdon |
| author_facet | Chen, Gong Moutinho, Abdon |
| contents | Consider the one-dimensional $L^2$ supercritical nonlinear Schrödinger equation \begin{equation} i\partial_{t}ψ+\partial^{2}_{x}ψ+\vert ψ\vert^{2k}ψ=0 \text{, $k>2$}. \end{equation} It is well known that solitary waves for this equation are unstable. In the pioneering work of Krieger and Schlag \cite{KriegerSchlag}, the asymptotic stability of a solitary wave was established on a codimension-one center-stable manifold. In the present paper, using linear estimates developed for one-dimensional matrix charge transfer models in our previous work, \cite{dispanalysis1}, we prove asymptotic stability of multi-solitons on a finite-codimension manifold for $k>\frac{11}{4}.$ |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_03637 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Asymptotic Stability of multi-solitons for $1$d Supercritical NLS Chen, Gong Moutinho, Abdon Analysis of PDEs Mathematical Physics 35B40, 35B35 Consider the one-dimensional $L^2$ supercritical nonlinear Schrödinger equation \begin{equation} i\partial_{t}ψ+\partial^{2}_{x}ψ+\vert ψ\vert^{2k}ψ=0 \text{, $k>2$}. \end{equation} It is well known that solitary waves for this equation are unstable. In the pioneering work of Krieger and Schlag \cite{KriegerSchlag}, the asymptotic stability of a solitary wave was established on a codimension-one center-stable manifold. In the present paper, using linear estimates developed for one-dimensional matrix charge transfer models in our previous work, \cite{dispanalysis1}, we prove asymptotic stability of multi-solitons on a finite-codimension manifold for $k>\frac{11}{4}.$ |
| title | Asymptotic Stability of multi-solitons for $1$d Supercritical NLS |
| topic | Analysis of PDEs Mathematical Physics 35B40, 35B35 |
| url | https://arxiv.org/abs/2509.03637 |