Geometric optics and boundary layers for Nonlinear Schrodinger equations
D. Chiron, F. Rousset
TL;DR
This paper rigorously justifies supercritical geometric optics approximations for the defocusing semiclassical nonlinear Schrödinger equation in small time, including boundary effects in half-space geometries.
Contribution
It extends geometric optics analysis to supercritical regimes and boundary conditions for a broad class of nonlinearities in nonlinear Schrödinger equations.
Findings
Validation of supercritical geometric optics in small time
Analysis of boundary effects with Neumann conditions
Applicable to a wide class of nonlinearities
Abstract
We justify supercritical geometric optics in small time for the defocusing semiclassical Nonlinear Schrodinger Equation for a large class of non-necessarily homogeneous nonlinearities. The case of a half-space with Neumann boundary condition is also studied.
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