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Caustics of interior scattering

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Abstract

The paper is devoted to geometrical optics of short linear waves in an inhomogeneous anisotropic medium. We find some typical singularities of caustics that arise due to the so-called interior scattering of waves, the mathematical theory of which was developed by V.I. Arnold in 1988.

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References

  1. V. I. Arnold, Singularities of Caustics and Wave Fronts (Phasis, Moscow, 1996); partial Engl. transl.: V. I. Arnold, Singularities of Caustics and Wave Fronts (Kluwer, Dordrecht, 1990).

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  2. L. D. Landau and E. M. Lifshitz, Theoretical Physics, Vol. 8: Electrodynamics of Continuous Media (Nauka, Moscow, 1992); Engl. transl. of the 1st ed.: L. D. Landau and E. M. Lifshitz, Electrodynamics of Continuous Media (Pergamon, Oxford, 1960).

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  3. I. A. Bogaevskii, “Singularities of the Propagation of Short Waves on the Plane,” Mat. Sb. 186(11), 35–52 (1995) [Sb. Math. 186, 1581–1597 (1995)].

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  4. I. A. Bogaevsky, “New Singularities and Perestroikas of Fronts of Linear Waves,” Moscow Math. J. 3(3), 807–821 (2003).

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  5. V. I. Arnold, “On the Interior Scattering of Waves, Defined by Hyperbolic Variational Principles,” J. Geom. Phys. 5(3), 305–315 (1988).

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Authors and Affiliations

  1. Moscow State University, Moscow, 119991, Russia

    I. A. Bogaevsky

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  1. I. A. Bogaevsky
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Original Russian Text © I.A. Bogaevsky, 2009, published in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2009, Vol. 267, pp. 7–13.

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Bogaevsky, I.A. Caustics of interior scattering. Proc. Steklov Inst. Math. 267, 1–7 (2009). https://doi.org/10.1134/S0081543809040014

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  • DOI: https://doi.org/10.1134/S0081543809040014

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