High frequency integrable regimes in nonlocal nonlinear optics. (English) Zbl 1121.78011

Moro, Antonio; Konopelchenko, Boris

J. Geom. Symmetry Phys. 7, 37-83 (2006).

From the authors’ 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 hierarchy.

Reviewer: Johannes Elschner (Berlin)

MSC:

78A60	Lasers, masers, optical bistability, nonlinear optics
78M35	Asymptotic analysis in optics and electromagnetic theory
35Q60	PDEs in connection with optics and electromagnetic theory
37K15	Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems

Keywords:

nonlinear Maxwell equations; nonlinear Schrödinger equation; high frequency limit; integrable regimes