87 citations · 1.6k across the 102 of their papers we have counts for
106 papers
Soliton Dynamics for the Cubic-Quintic Nonlinear Schrödinger Equation with a Potential
Alex H. Ardila, Rémi Carles
We study the semiclassical dynamics of solitary waves for the three-dimensional cubic--quintic nonlinear Schrödinger equation with an external potential. For initial data given by…
Dynamics near the origin of the long range scattering for the one-dimensional Schrodinger equation
Remi Carles
We consider the cubic Schrodinger equation on the line, for which the scattering theory requires modifications due to long range effects. We revisit the construction of the modifie…
On nonlinear effects in multiphase WKB analysis for the nonlinear Schrodinger equation
Remi Carles
We consider the Schrodinger equation with an external potential and a cubic nonlinearity, in the semiclassical limit. The initial data are sums of WKB states, with smooth phases an…
Pathological set with loss of regularity for nonlinear Schr{ö}dinger equations
Rémi Carles, Louise Gassot
We consider the mass-supercritical, defocusing, nonlinear Schr{ö}dinger equation. We prove loss of regularity in arbitrarily short times for regularized initial data belonging to a…
Logarithmic Gross-Pitaevskii equation
Rémi Carles, Guillaume Ferriere
We consider the Schr{ö}dinger equation with a logarithmic nonlinearty and non-trivial boundary conditions at infinity. We prove that the Cauchy problem is globally well posed in th…
On the Cauchy problem for the Hartree approximation in quantum dynamics
Rémi Carles, Clotilde Fermanian Kammerer, Caroline Lasser
We prove existence and uniqueness results for the time-dependent Hartree approximation arising in quantum dynamics. The Hartree equations of motion form a coupled system of nonline…