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Article Dans Une Revue Annales I.H.P., Analyse non linéaire Année : 2003

Semi-classical Schrodinger equations with harmonic potential and nonlinear perturbation

Rémi Carles

Résumé

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.
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Dates et versions

hal-00132804 , version 1 (22-02-2007)

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Rémi Carles. Semi-classical Schrodinger equations with harmonic potential and nonlinear perturbation. Annales I.H.P., Analyse non linéaire, 2003, 20, pp.no. 3, 501-542. ⟨10.1016/S0294-1449(02)00027-6⟩. ⟨hal-00132804⟩

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