Integrable equations in nonlinear geometrical optics

B. Konopelchenko*, A. Moro

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

16 Citations (Scopus)

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 ∂̄3-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.

Original languageEnglish
Pages (from-to)325-352
Number of pages28
JournalStudies in Applied Mathematics
Volume113
Issue number4
DOIs
Publication statusPublished - Nov 2004

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