Reviews of topical problems

Singularities of continuation of wave fields

 a,  b,  b
a Moscow Technical University of Communications and Informatics, ul. Aviamotornaya 8a, Moscow, 111024, Russian Federation
b Lomonosov Moscow State University, Vorobevy Gory, Moscow, 119991, Russian Federation

The state of the art of the problem of the analytical continuation of wave fields is reviewed. The problem is a multidisciplinary subject which involves radiophysics, acoustics, and optics on the one hand, and mathematical physics and the theory of differential equation, on the other. The qualitative aspects of the problem are examined. A computational algorithm for field singularities is given. The relation between the singularities and the ’computational catastrophes’ of scattering models is discussed. To illustrate the theoretical material, numerous examples are discussed in great detail.

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Fulltext is also available at DOI: 10.1070/PU1996v039n12ABEH000184
PACS: 02.30.−f, 02.90.+p, 41.20.−q, 41.20.Jb (all)
DOI: 10.1070/PU1996v039n12ABEH000184
Citation: Kyurkchan A G, Sternin B Yu, Shatalov V E "Singularities of continuation of wave fields" Phys. Usp. 39 1221–1242 (1996)
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Оригинал: Кюркчан А Г, Стернин Б Ю, Шаталов В Е «Особенности продолжения волновых полей» УФН 166 1285–1308 (1996); DOI: 10.3367/UFNr.0166.199612b.1285

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