Nonlinear Schrödinger equations with repulsive harmonic potential and applications - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue SIAM Journal on Mathematical Analysis Année : 2003

Nonlinear Schrödinger equations with repulsive harmonic potential and applications

Résumé

We study the Cauchy problem for Schrödinger equations with repulsive quadratic potential and power-like nonlinearity. The local problem is well-posed in the same space as that used when a confining harmonic potential is involved. For a defocusing nonlinearity, it is globally well-posed, and a scattering theory is available, with no long range effect for any superlinear nonlinearity. When the nonlinearity is focusing, we prove that choosing the harmonic potential sufficiently strong prevents blow-up in finite time. Thanks to quadratic potentials, we provide a method to anticipate, delay, or prevent wave collapse; this mechanism is explicit for critical nonlinearity.

Dates et versions

hal-00004966 , version 1 (24-05-2005)

Identifiants

Citer

Rémi Carles. Nonlinear Schrödinger equations with repulsive harmonic potential and applications. SIAM Journal on Mathematical Analysis, 2003, 35, pp.823-843. ⟨10.1137/S0036141002416936⟩. ⟨hal-00004966⟩

Collections

CNRS TDS-MACS
34 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More