On asymptotic stability of solitons for nonlinear Sch\"odinger equation
Mathematical Physics
2010-12-15 v2 Analysis of PDEs
math.MP
Abstract
The long-time asymptotics is analyzed for finite energy solutions of the 1D Schr\"odinger equation coupled to a nonlinear oscillator; mathematically the system under study is a nonlinear Schr\"odinger equation, whose nonlinear term includes a Dirac delta. The coupled system is invariant with respect to the phase rotation group U(1). This article, which extends the results of a previous one, provides a proof of asymptotic stability of solitary wave solutions in the case that the linearization contains a single discrete oscillatory mode satisfying a non-degeneracy assumption of the type known as the Fermi Golden Rule.
Keywords
Cite
@article{arxiv.0807.1878,
title = {On asymptotic stability of solitons for nonlinear Sch\"odinger equation},
author = {A. I. Komech and E. A. Kopylova and D. Stuart},
journal= {arXiv preprint arXiv:0807.1878},
year = {2010}
}