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Download fileGeometric Optics and Instability for NLS and Davey-Stewartson Models
journal contribution
posted on 2013-11-26, 00:00 authored by Remi Carles, Eric Dumas, Christof SparberWe study the interaction of (slowly modulated) high frequency
waves for multi-dimensional nonlinear Schr odinger equations with gauge invariant
power-law nonlinearities and nonlocal perturbations. The model includes
the Davey{Stewartson system in its elliptic-elliptic and hyperbolic-elliptic variant.
Our analysis reveals a new localization phenomenon for nonlocal 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 in
ation with in nite loss of regularity by a constructive approach.