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arXiv · 0807.1878

On asymptotic stability of solitons for nonlinear Sch\"odinger equation

A. I. Komech·E. A. Kopylova·D. Stuart
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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.

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A. I. Komech, E. A. Kopylova, D. Stuart. 2008-07-11. On asymptotic stability of solitons for nonlinear Sch\"odinger equation. https://arxiv.org/abs/0807.1878

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