Asymptotic Stability of multi-solitons for $1$d Supercritical NLS
Abstract
Consider the one-dimensional supercritical nonlinear Schr\"odinger equation \begin{equation} i\partial_{t}\psi+\partial^{2}_{x}\psi+\vert \psi\vert^{2k}\psi=0 \text{, }. \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
Keywords
Cite
@article{arxiv.2509.03637,
title = {Asymptotic Stability of multi-solitons for $1$d Supercritical NLS},
author = {Gong Chen and Abdon Moutinho},
journal= {arXiv preprint arXiv:2509.03637},
year = {2025}
}
Comments
Version 3: REMOVAL OF SOME HYPOTHESES, REMOVAL OF CONDITION OF SEPARATION ON SPEEDS, IMPROVED ESTIMATES FOR THE MODIFIED SCATTERING WAVE OPERATOR OF THE REMAINDER. 82 pages. Keywords: Scattering,, Asymptotic Stability on $H^{1}$ norm, 1d supercritical NLS, multi-solitons, non-integrable, H1 norm, Center-stable Manifold; Mistype errors corrected; Comments are welcome