Semi-classical Schrodinger equations with harmonic potential and nonlinear perturbation
Idioma
en
Article de revue
Este ítem está publicado en
Annales I.H.P., Analyse non linéaire. 2003, vol. 20, p. no. 3, 501-542
Resumen en inglés
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, ...Leer más >
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.< Leer menos
Palabras clave en inglés
Harmonic oscillator
nonlinear Schrodinger equation
scattering theory
Maslov index
Orígen
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