41 citations · 125 across the 13 of their papers we have counts for
5 papers · 2 filters
Linear vs. nonlinear effects for nonlinear Schrodinger equations with potential
Remi Carles
We review some recent results on nonlinear Schrodinger equations with potential, with emphasis on the case where the potential is a second order polynomial, for which the interacti…
(Semi)classical limit of the Hartree equation with harmonic potential
Remi Carles, Norbert Mauser, Hans Peter Stimming
Nonlinear Schrodinger Equations (NLS) of the Hartree type occur in the modeling of quantum semiconductor devices. Their "semiclassical" limit of vanishing (scaled) Planck constant…
Global existence results for nonlinear Schrodinger equations with quadratic potentials
Remi Carles
We prove that no finite time blow up can occur for nonlinear Schroedinger equations with quadratic potentials, provided that the potential has a sufficiently strong repulsive compo…
On the role of quadratic oscillations in nonlinear Schroedinger equations II. The -critical case
Remi Carles, Sahbi Keraani
We consider a nonlinear semi-classical Schroedinger equation for which quadratic oscillations lead to focusing at one point, described by a nonlinear scattering operator. The relev…
Scattering theory for the Schrodinger equation with repulsive potential
Jean-Francois Bony, Remi Carles, Dietrich Haefner +1
We consider the scattering theory for the Schrodinger equation with as a reference Hamiltonian, for , in any space dimension. We prove that when this Hamilto…