On asymptotic stability of solitary waves for nonlinear Schrödinger equations
type: Item
instance of: scholarly article
title: On asymptotic stability of solitary waves for nonlinear Schrödinger equations
zbMATH Open document ID: 1028.35139
DOI: 10.1016/S0294-1449(02)00018-5
author: V. S. Buslaev
author: Catherine Sulem
published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire
publication date: 2003-06-09T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/78586
review text: The authors analyse the long-time behaviour of solutions to the nonlinear Schrödinger equation in 1D space dimension for initial conditions in a small neighbourhood of a stable solitary wave. They use the spectral decomposition of the solution on the eigenspaces associated to the discrete and continuous spectrum of the linearized operator near the solitary wave. Using some hypothesis on the structure of the spectrum of the linearized operator, the authors prove that, asymptotically in time, the solution decomposes into a solitary wave with slightly modified parameters and a dispersive part described by the Schrödinger equation.
Mathematics Subject Classification ID: 35Q55
Mathematics Subject Classification ID: 37K40
zbMATH DE Number: 1924840
zbMATH Keywords: nonlinear Schrödinger equations
zbMATH Keywords: solitary waves
zbMATH Keywords: asymptotic stability
Wikidata QID: Q55950863
reviewed by: I. V. Andrianov
MaRDI profile type: Publication
cites work: Orbital stability of standing waves for some nonlinear Schrödinger equations
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cites work: Q4853576
cites work: Stabilization of solutions to nonlinear Schrödinger equations
cites work: Perturbation theory for infinite-dimensional integrable systems on the line. A case study
cites work: On a class of nonlinear Schrödinger equations. I. The Cauchy problem, general case
cites work: Stability theory of solitary waves in the presence of symmetry. II
cites work: The nonlinear Schrödinger equation and the nonlinear heat equation reduction to linear form
cites work: On the formation of singularities in solutions of the critical nonlinear Schrödinger equation
cites work: Internal modes of envelope solitons
cites work: Multichannel nonlinear scattering for nonintegrable equations. II: The case of anisotropic potentials and data
cites work: Resonances, radiation damping and instability in Hamiltonian nonlinear wave equations
cites work: Nonlinear scattering theory at low energy: Sequel
cites work: The nonlinear Schrödinger equation. Self-focusing and wave collapse
cites work: Lyapunov stability of ground states of nonlinear dispersive evolution equations
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description: scientific article; zbMATH DE number 1924840