Geometrical optics in nonlinear media and integrable equations

It is shown that the geometrical optics limit of the Maxwell equations for certain nonlinear media with slow variation along one axis and particular dependence of the dielectric constant on frequency and fields gives rise to the dispersionless Veselov-Novikov equation for the refractive index. It is demonstrated that the dispersionless Veselov-Novikov hierarchy is amenable to the quasiclassical ∂ ̄-dressing method. A connection is noted between the geometrical optics phenomena under consideration and the quasiconformal mappings on the plane.