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2006 High Frequency Integrable Regimes in Nonlocal Nonlinear Optics
Antonio Moro, Boris Konopelchenko
J. Geom. Symmetry Phys. 7: 37-83 (2006). DOI: 10.7546/jgsp-7-2006-37-83

Abstract

We consider an integrable model which describes light beams propagating in nonlocal nonlinear media of Cole-Cole type. The model is derived as high frequency limit of both Maxwell equations and the nonlocal nonlinear Schrödinger equation. We demonstrate that for a general form of nonlinearity there exist selfguided light beams. In high frequency limit nonlocal perturbations can be seen as a class of phase deformation along one direction. We study in detail nonlocal perturbations described by the dispersionless Veselov-Novikov (dVN) hierarchy. The dVN hierarchy is analyzed by the reduction method based on symmetry constraints and by the quasiclassical $\bar{\partial}-$ dressing method. Quasiclassical $\bar{\partial}-$dressing method reveals a connection between nonlocal nonlinear geometric optics and the theory of quasiconformal mappings of the plane.

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Antonio Moro. Boris Konopelchenko. "High Frequency Integrable Regimes in Nonlocal Nonlinear Optics." J. Geom. Symmetry Phys. 7 37 - 83, 2006. https://doi.org/10.7546/jgsp-7-2006-37-83

Information

Published: 2006
First available in Project Euclid: 20 May 2017

zbMATH: 1121.78011
MathSciNet: MR2290124
Digital Object Identifier: 10.7546/jgsp-7-2006-37-83

Rights: Copyright © 2006 Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences

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