Semi-classical Schrödinger equations with harmonic potential and nonlinear perturbation
The author studies the perturbation by a nonlinear term of semi-classical Schrödinger equation with isotropic harmonic potential. The author proves that if the scaling of this perturbation is critical, each focus crossing is described by a nonlinear scattering operator. The proofs of the main results are based on two operators well adapted to Schrödinger equations with harmonic potential and on suitable Strichartz inequalities.
scientific article; zbMATH DE number 1924842