Integrable Equations in Nonlinear Geometrical Optics

Konopelchenko, Boris and Moro, Antonio (2004) Integrable Equations in Nonlinear Geometrical Optics. Studies in Applied Mathematics, 113 (4). pp. 325-352. ISSN 0022-2526

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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 inline image‐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.

Item Type: Article
Subjects: G100 Mathematics
Department: Faculties > Engineering and Environment > Mathematics, Physics and Electrical Engineering
Depositing User: Becky Skoyles
Date Deposited: 19 Jul 2018 14:42
Last Modified: 11 Oct 2019 19:45

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