Geometric optics and boundary layers for Nonlinear Schrodinger equations

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.

44 pages

References in corpus (3)

• Low-dimensional Bose liquids: beyond the Gross-Pitaevskii approximation
• Loss of regularity for supercritical nonlinear Schrodinger equations
• Boundary layers and emitted excitations in nonlinear Schrodinger superflow past a disk

Cited by in corpus (7)

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• On Fourier time-splitting methods for nonlinear Schrodinger equations in the semi-classical limit II. Analytic regularity
• An asymptotic preserving approach for nonlinear Schrodinger equation in the semiclassical limit
• WKB analysis of the Logarithmic Nonlinear Schrodinger Equation in an analytic framework
• WKB analysis of generalized derivative nonlinear Schrodinger equations without hyperbolicity
• Semi-classical analysis with new Galilean transformations for a Gross--Pitaevskii system with non-zero conditions at infinity
• On nonlinear effects in multiphase WKB analysis for the nonlinear Schrodinger equation