A revision of "On asymptotic stability in energy space of ground states of NLS in 1D"

Abstract

We transpose work by T.Mizumachi to prove smoothing estimates for dispersive solutions of the linearization at a ground state of a Nonlinear Schrödinger equation (NLS) in 1D. As an application we extend to dimension 1D a result on asymptotic stability of ground states of NLS proved by Cuccagna & Mizumachi for dimensions $\ge 3$

This is a revision of the author's paper "On asymptotic stability in energy space of ground states of NLS in 1D" which appeared in J.Diff.Equations 245 (2008) pp 653-691. We correct an error in Lemma 5.4 in that paper and we simplify the smoothing argument

References in corpus (2)

• Asymptotic stability of N-soliton states of NLS
• Asymptotic stability of small solitons for 2D Nonlinear Schrödinger equations with potential

Cited by in corpus (3)

• On asymptotic stability of standing waves of discrete Schrödinger equation in $\mathbb{Z}$
• On asymptotic stability of ground states of NLS with a finite bands periodic potential in 1D
• On instability of some approximate periodic solutions for the full nonlinear Schrödinger equation