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Geometric Optics and Instability for NLS and Davey-Stewartson Models

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journal contribution
posted on 26.11.2013, 00:00 by Remi Carles, Eric Dumas, Christof Sparber
We 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.

Funding

This work was supported by the French ANR project R.A.S. (ANR-08-JCJC-0124-01) and by the Royal Society Research fellowship of C. Sparber

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Publisher Statement

Post print version of article may differ from published version. The definitive version is available through European Mathematical Society at DOI:10.4171/JEMS/350

Publisher

European Mathematical Society

Language

en_US

issn

1435-9855

Issue date

01/06/2012

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