Critical nonlinear Schrödinger equations with and without harmonic potential - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Mathematical Models and Methods in Applied Sciences Année : 2002

Critical nonlinear Schrödinger equations with and without harmonic potential

Résumé

We use a change of variables that turns the critical nonlinear Schrödinger equation into the critical nonlinear Schrödinger equation with isotropic harmonic potential, in any space dimension. This change of variables is isometric on $L^2$, and bijective on some time intervals. Using the known results for the critical nonlinear Schrödinger equation, this provides information for the properties of Bose-Einstein condensate in space dimension one and two. We discuss in particular the wave collapse phenomenon.

Dates et versions

hal-00004964 , version 1 (24-05-2005)

Identifiants

Citer

Rémi Carles. Critical nonlinear Schrödinger equations with and without harmonic potential. Mathematical Models and Methods in Applied Sciences, 2002, 12, pp.1513-1523. ⟨hal-00004964⟩

Collections

CNRS
34 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More