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On asymptotic stability of solitary waves in Schrödinger equation coupled to nonlinear oscillator
| Venue: | Comm. Partial Diff. Equations |
| Citations: | 3 - 0 self |
BibTeX
@ARTICLE{Buslaev_onasymptotic,
author = {V. S. Buslaev and A. I. Komech and E. A. Kopylova and D. Stuart},
title = {On asymptotic stability of solitary waves in Schrödinger equation coupled to nonlinear oscillator},
journal = {Comm. Partial Diff. Equations},
year = {},
pages = {669--705}
}
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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. 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 Schrödinger equation. The proofs use the strategy of Buslaev-Perelman [2, 3]: the linerization of the dynamics on the solitary manifold, the symplectic orthogonal projection, method of majorants, etc. 1Supported partly by RFBR research grants 05-0101076 and 05-01002944.
Keyphrases
solitary wave asymptotic stability schr dinger equation rfbr research grant symplectic orthogonal projection nonlinear oscillator initial state dispersive wave solitary manifold schro dinger equation finite energy solution free schro dinger equation phase rotation group long-time asymptotics coupled system
