Evolution of wave field jumps near caustics (elementary approach)
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 45, Tome 438 (2015), pp. 46-72 Cet article a éte moissonné depuis la source Math-Net.Ru

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The Poisson formula solving a $3$-dim Cauchy problem for the wave equation is applied to study behavior of the wave field singularities (jumps) near caustics in the $2$-dim and $3$-dim cases. The approach of quite elementary character enables one to describe the focusing effects in detail.
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M. I. Belishev; A. F. Vakulenko; A. Ya. Kazakov. Evolution of wave field jumps near caustics (elementary approach). Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 45, Tome 438 (2015), pp. 46-72. http://geodesic.mathdoc.fr/item/ZNSL_2015_438_a3/

[1] V. I. Arnold, A. N. Varchenko, S. M. Gusein-Zade, Osobennosti differentsiruemykh otobrazhenii, v. 1, Nauka, M., 1982 | MR

[2] V. M. Babich, “Rasprostranenie nestatsionarnykh voln i kaustiki. Dinamicheskie problemy v teorii uprugosti. IV”, Uchenye zapiski LGU, 32, Leningrad, 1958, 228–259

[3] V. M. Babich, “Analiticheskii kharakter polya nestatsionarnoi volny v okrestnosti kaustiki”, Problemy dinamicheskoi teorii rasprostraneniya seismicheskikh voln, Izd. LGU, Leningrad, 1961, 115–144 | MR

[4] V. M. Babich, V. S. Buldyrev, Asimptoticheskie metody v zadachakh difraktsii korotkikh voln, M., 1972

[5] Yu. A. Kravtsov, Yu. I. Orlov, Caustics, catastrophes and wave fields, Springer-Verlag, Berlin–Heidelberg–New-York, 1999 | MR | Zbl

[6] V. S. Vladimirov, Uravneniya matematicheskoi fiziki, Nauka, M., 1971 | MR