High frequency integrable regimes in nonlocal nonlinear optics

Antonio Moro*, Boris Konopelchenko

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)

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

Original languageEnglish
Pages (from-to)37-83
Number of pages47
JournalJournal of Geometry and Symmetry in Physics
Volume7
DOIs
Publication statusPublished - 2006
Externally publishedYes

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