Geometrical optics in nonlinear media and integrable equations

Details Geometrical optics in nonlinear media and integrable equations Geometrical optics in nonlinear media and integrable equations

2003-12-30

arxiv.org/abs/nlin/0312069v2

Jour.Phys.A:Math.Gen., vol. 37, pp. L105-L111, (2004)

Nonlinear Sciences

Exactly Solvable and Integrable Systems

10 pages, misprints corrected

Scientific paper

10.1088/0305-4470/37/10/L01

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 dielectric constant on the frequency and fields gives rise to the dispersionless Veselov-Novikov equation for refractive index. It is demonstrated that the last one is amenable to the quasiclassical DBAR-dressing method. A connection is noted between geometrical optics phenomena under consideration and quasiconformal mappings on the plane.

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