Geometric optics and instability for NLS and Davey-Stewartson models

Abstract

We study the interaction of (slowly modulated) high frequency waves for multi-dimensional nonlinear Schrodinger equations with gauge invariant power-law nonlinearities and non-local perturbations. The model includes the Davey--Stewartson system in its elliptic-elliptic and hyperbolic-elliptic variant. Our analysis reveals a new localization phenomenon for non-local perturbations in the high frequency regime and allows us to infer strong instability results on the Cauchy problem in negative order Sobolev spaces, where we prove norm inflation with infinite loss of regularity by a constructive approach.

33 pages

References in corpus (2)

• Instability of the periodic nonlinear Schrodinger equation
• High-frequency averaging in semi-classical Hartree-type equations

Cited by in corpus (9)

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• On nonlinear effects in multiphase WKB analysis for the nonlinear Schrodinger equation
• Norm inflation for BBM equation in Fourier amalgam and Wiener amalgam spaces with negative regularity
• Nonlinear Schrodinger equation and frequency saturation