Semi-classical Schrödinger equations with harmonic potential and nonlinear perturbation
type: Item
instance of: scholarly article
title: Semi-classical Schrödinger equations with harmonic potential and nonlinear perturbation
zbMATH Open document ID: 1031.35119
DOI: 10.1016/S0294-1449(02)00027-6
author: Rémi Carles
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/78588
review text: The author studies the perturbation by a nonlinear term of semi-classical Schrödinger equation with isotropic harmonic potential. The author proves that if the scaling of this perturbation is critical, each focus crossing is described by a nonlinear scattering operator. The proofs of the main results are based on two operators well adapted to Schrödinger equations with harmonic potential and on suitable Strichartz inequalities.
Mathematics Subject Classification ID: 35Q40
Mathematics Subject Classification ID: 81Q20
Mathematics Subject Classification ID: 35P25
zbMATH DE Number: 1924842
zbMATH Keywords: semi-classical Schrödinger equation
zbMATH Keywords: harmonic potential
zbMATH Keywords: nonlinear perturbation
zbMATH Keywords: Strichartz inequalities
reviewed by: Laura Iulia Aniţa
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1924842