Semi-classical Schrodinger equations with harmonic potential and nonlinear perturbation
Langue
en
Article de revue
Ce document a été publié dans
Annales I.H.P., Analyse non linéaire. 2003, vol. 20, p. no. 3, 501-542
Résumé en anglais
Solutions of semi-classical Schrodinger equation with isotropic harmonic potential focus periodically in time. We study the perturbation of this equation by a nonlinear term. If the scaling of this perturbation is critical, ...Lire la suite >
Solutions of semi-classical Schrodinger equation with isotropic harmonic potential focus periodically in time. We study the perturbation of this equation by a nonlinear term. If the scaling of this perturbation is critical, each focus crossing is described by a nonlinear scattering operator, which is therefore iterated as many times as the solution passes through a focus. The study of this nonlinear problem is made possible by the introduction of two operators well adapted to Schrodinger equations with harmonic potential, and by suitable Strichartz inequalities.< Réduire
Mots clés en anglais
Harmonic oscillator
nonlinear Schrodinger equation
scattering theory
Maslov index
Origine
Importé de halUnités de recherche