249 citations · 684 across the 32 of their papers we have counts for
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math.AP2007★ 10 cited
WKB analysis for the Gross-Pitaevskii equation with non-trivial boundary conditions at infinity
Thomas Alazard, Rémi Carles
We consider the semi-classical limit for the Gross-Pitaevskii equation. In order to consider non-trivial boundary conditions at infinity, we work in Zhidkov spaces rather than in S…
math.AP2007★ 18 cited
Supercritical geometric optics for nonlinear Schrodinger equations
Thomas Alazard, Rémi Carles
We consider the small time semi-classical limit for nonlinear Schrodinger equations with defocusing, smooth, nonlinearity. For a super-cubic nonlinearity, the limiting system is no…
math.AP2007★ 39 cited
Loss of regularity for supercritical nonlinear Schrodinger equations
Thomas Alazard, Rémi Carles
We consider the nonlinear Schrodinger equation with defocusing, smooth, nonlinearity. Below the critical Sobolev regularity, it is known that the Cauchy problem is ill-posed. We sh…