Integrable equations in nonlinear geometrical optics

Details Integrable equations in nonlinear geometrical optics Integrable equations in nonlinear geometrical optics

2004-03-29

arxiv.org/abs/nlin/0403051v1

Stud. Appl. Math. vol. 113, pp.325-352 (2004)

Nonlinear Sciences

Exactly Solvable and Integrable Systems

33 pages, 7 figures

Scientific paper

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 DBAR-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.

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