On asymptotic stability of solitons       in a nonlinear Schrödinger equation

Alexander Komech; Elena Kopylova; David Stuart

doi:10.3934/cpaa.2012.11.1063

Article Contents

2012, Volume 11, Issue 3: 1063-1079. Doi: 10.3934/cpaa.2012.11.1063

This issue Previous Article A faithful symbolic extension Next Article Low regularity well-posedness for the 3D Klein - Gordon - Schrödinger system

On asymptotic stability of solitons in a nonlinear Schrödinger equation

1.
Faculty of Mathematics of Vienna University, Vienna
2.
IITP RAS, Moscow
3.
Centre for Mathematical Sciences, Cambridge

Received: November 2010

Revised: May 2011

Published: May 2012

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Abstract

The long-time asymptotics is analyzed for finite energy solutions of the 1D Schrödinger equation coupled to a nonlinear oscillator through a localized nonlinearity. The coupled system is $U(1)$ invariant. This article, which extends the results of a previous one, provides a proof of asymptotic stability of the 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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Mathematics Subject Classification: 35Q55, 37K40.

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References

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