Integrable Equations in Nonlinear Geometrical Optics

Abstract

Geometrical optics limit of the Maxwell equations for nonlinear media with the Cole–Cole dependence of dielectric function and magnetic permeability on the frequency is considered. It is shown that for media with slow variation along one axis such a limit gives rise to the dispersionless Veselov–Novikov equation for the refractive index. It is demonstrated that the Veselov–Novikov hierarchy is amenable to the quasiclassical ‐dressing method. Under more specific requirements for the media, one gets the dispersionless Kadomtsev–Petviashvili equation. Geometrical optics interpretation of some solutions of the above equations is discussed.