High frequency integrable regimes in nonlocal nonlinear optics

Details High frequency integrable regimes in nonlocal nonlinear optics High frequency integrable regimes in nonlocal nonlinear optics

2006-03-27

arxiv.org/abs/nlin/0603062v1

Journal of Geometry and Symmetry in Physics, 7, pp. 37-83 (2006)

Nonlinear Sciences

Exactly Solvable and Integrable Systems

45 pages, 4 figures

Scientific paper

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 Schroedinger 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 Dbar-dressing method. Quasiclassical Dbar-dressing method reveals a connection between nonlocal nonlinear geometric optics and the theory of quasiconformal mappings of the plane.

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