Geometric optics and instability for NLS and Davey-Stewartson models

Carles, Rémi, Dumas, Eric, and Sparber, Christof. "Geometric optics and instability for NLS and Davey-Stewartson models." Journal of the European Mathematical Society 014.6 (2012): 1885-1921. <http://eudml.org/doc/277347>.

@article{Carles2012,
abstract = {We study the interaction of (slowly modulated) high frequency waves for multi-dimensional nonlinear Schrödinger 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.},
author = {Carles, Rémi, Dumas, Eric, Sparber, Christof},
journal = {Journal of the European Mathematical Society},
keywords = {nonlinear Schrödinger equation; Davey-Stewartson system; geometric optics; instability; nonlinear Schrödinger equation; Davey-Stewartson system; geometric optics; instability},
language = {eng},
number = {6},
pages = {1885-1921},
publisher = {European Mathematical Society Publishing House},
title = {Geometric optics and instability for NLS and Davey-Stewartson models},
url = {http://eudml.org/doc/277347},
volume = {014},
year = {2012},
}

TY - JOUR
AU - Carles, Rémi
AU - Dumas, Eric
AU - Sparber, Christof
TI - Geometric optics and instability for NLS and Davey-Stewartson models
JO - Journal of the European Mathematical Society
PY - 2012
PB - European Mathematical Society Publishing House
VL - 014
IS - 6
SP - 1885
EP - 1921
AB - We study the interaction of (slowly modulated) high frequency waves for multi-dimensional nonlinear Schrödinger 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.
LA - eng
KW - nonlinear Schrödinger equation; Davey-Stewartson system; geometric optics; instability; nonlinear Schrödinger equation; Davey-Stewartson system; geometric optics; instability
UR - http://eudml.org/doc/277347
ER -