87 citations · 1.6k across the 102 of their papers we have counts for
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On the semi-classical limit for the nonlinear Schrodinger equation
Rémi Carles
We review some results concerning the semi-classical limit for the nonlinear Schrodinger equation, with or without an external potential. We consider initial data which are either…
Semi-classical limit of Schrodinger-Poisson equations in space dimension at least 3
Thomas Alazard, Rémi Carles
We prove the existence of solutions to the Schrodinger-Poisson system on a time interval independent of the Planck constant, when the doping profile does not necessarily decrease a…
On the Cauchy problem in Sobolev spaces for nonlinear Schrodinger equations with potential
Rémi Carles
We consider the Cauchy problem for nonlinear Schrodinger equations in the presence of a smooth, possibly unbounded, potential. No assumption is made on the sign of the potential. I…
Scattering theory for radial nonlinear Schrödinger equations on hyperbolic space
Valeria Banica, Rémi Carles, Gigliola Staffilani
We study the long time behavior of radial solutions to nonlinear Schrödinger equations on hyperbolic space. We show that the usual distinction between short range and long range no…
Monotonicity properties of blow-up time for nonlinear Schrödinger equation: numerical tests
Christophe Besse, Rémi Carles, Norbert Mauser +1
We consider the focusing nonlinear Schrödinger equation, in the -critical and supercritical cases. We investigate numerically the dependence of the blow-up time on a parameter…
WKB analysis for nonlinear Schrödinger equations with potential
Rémi Carles
We justify the WKB analysis for the semiclassical nonlinear Schrödinger equation with a subquadratic potential. This concerns subcritical, critical, and supercritical cases as far…