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 $\ge 3$

arXiv commentThis 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 (7)

• Selection of the ground state for nonlinear Schroedinger equations
• Asymptotic stability of N-soliton states of NLS
• On asymptotic stability in energy space of ground states for Nonlinear Schrödinger equations
• Asymptotic stability of small solitons to 1D NLS with potential
• Relaxation of Excited States in Nonlinear Schrödinger Equations
• Asymptotic stability of small solitons for 2D Nonlinear Schrödinger equations with potential
• Asymptotic Dynamics of Nonlinear Schrodinger Equations: Resonance Dominated and Radiation Dominated Solutions

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