On Asymptotic Stability of Solitary Waves in a Nonlinear Schrödinger Equation

Preprint

4 February 2007

preprint
Published by arXiv in arXiv

https://doi.org/10.48550/arXiv.math-ph/0702013

Abstract

The long-time asymptotics is analyzed for finite energy solutions of the 1D Schr\"odinger equation coupled to a nonlinear oscillator. The coupled system is invariant with respect to the phase rotation group U(1). For initial states close to a solitary wave, the solution converges to a sum of another solitary wave and dispersive wave which is a solution to the free Schr\"odinger equation. The proofs use the strategy of Buslaev-Perelman: the linerization of the dynamics on the solitary manifold, the symplectic orthogonal projection and method of majorants.

Keywords

ASYMPTOTIC STABILITY
ODINGER EQUATION
DISPERSIVE WAVE
NONLINEAR SCHR
SOLITARY WAVE
WAVE
SCHR

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Version 1, 2007-02-04, ArXiv

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