Asymptotic Stability of multi-solitons for 1d Supercritical NLS

2025/09/03 by Chen, Gong, Moutinho, Abdon · 1 citation
#35B35 #35B40 #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2509.03637

Abstract

Consider the one-dimensional L² supercritical nonlinear Schrödinger equation i∂_tψ+∂²_xψ+\vert ψ\vert^2kψ=0 , kgt;2. It is well known that solitary waves for this equation are unstable. In the pioneering work of Krieger and Schlag \citeKriegerSchlag, 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, \citedispanalysis1, we prove asymptotic stability of multi-solitons on a finite-codimension manifold for k>(11)/(4).

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• Weakly localized states of one dimensional Schrodinger equations have localized energy

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