Geometric Optics and Boundary Layers for Nonlinear Schrödinger Equations

David Chiron (1) , Rousset Frédéric (2)

1 JAD - Laboratoire Jean Alexandre Dieudonné
2 LJAD - Laboratoire Jean Alexandre Dieudonné

We justify supercritical geometric optics in small time for the defocusing semiclassical Nonlinear Schrödinger Equation for a large class of non-necessarily homogeneous nonlinearities. The case of a half-space with Neumann boundary condition is also studied.

Mots clés: semiclassical limit

Domaines: Equations aux dérivées partielles [math.AP]

David Chiron, Rousset Frédéric. Geometric Optics and Boundary Layers for Nonlinear Schrödinger Equations. Communications in Mathematical Physics, 2009, 288 (2), pp.503-546. ⟨10.1007/s00220-009-0748-x⟩. ⟨hal-00809289⟩