Geodesic
Geometric optics and instability for NLS and Davey–Stewartson models
Journal of the European Mathematical Society, Tome 14 (2012) no. 6, pp. 1885-1921

Voir la notice de l'article provenant de la source EMS Press

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 variants. 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 inflation with infinite loss of regularity by a constructive approach.
DOI : 10.4171/jems/350
Classification : 35-XX, 00-XX
Keywords: Nonlinear Schrödinger equation, Davey–Stewartson system, geometric optics, instability 
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     author = {R\'emi Carles and Eric Dumas and Christof Sparber},
     title = {Geometric optics and instability for {NLS} and {Davey{\textendash}Stewartson} models},
     journal = {Journal of the European Mathematical Society},
     pages = {1885--1921},
     publisher = {mathdoc},
     volume = {14},
     number = {6},
     year = {2012},
     doi = {10.4171/jems/350},
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Rémi Carles; Eric Dumas; Christof Sparber. Geometric optics and instability for NLS and Davey–Stewartson models. Journal of the European Mathematical Society, Tome 14 (2012) no. 6, pp. 1885-1921. doi: 10.4171/jems/350

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