Singularities of continuation of wave fields

A.G. Kyurkchan^a, B.Yu. Sternin^b, V.E. Shatalov^b
^aMoscow Technical University of Communications and Informatics, ul. Aviamotornaya 8a, Moscow, 111024, Russian Federation
^bLomonosov 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.

PACS: 02.30.−f, 02.90.+p, 41.20.−q, 41.20.Jb (all)
DOI: 10.1070/PU1996v039n12ABEH000184
URL: https://ufn.ru/en/articles/1996/12/b/
Web of Science

A1996WE26100002
Citation: Kyurkchan A G, Sternin B Yu, Shatalov V E "Singularities of continuation of wave fields" Phys. Usp. 39 1221–1242 (1996)

BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks

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

References (63) Cited by (59) Similar articles (20) ↓

N.M. Astaf’eva “Wavelet analysis: basic theory and some applications” 39 1085–1108 (1996)
V.B. Shteinshleiger “Nonlinear scattering of radio waves by metallic objects” 27 60–68 (1984)
V.I. Arnol’d “Singularities, bifurcations, and catastrophes” 26 1025–1037 (1983)
V.S. Dotsenko “Universal randomness” 54 259–280 (2011)
A.G. Fokin “Macroscopic conductivity of random inhomogeneous media. Calculation methods” 39 1009–1032 (1996)
B.Z. Katsenelenbaum, E.N. Korshunova et al “Chiral electromagnetic objects” 40 1149–1160 (1997)
D.N. Razdoburdin, V.V. Zhuravlev “Transient dynamics of perturbations in astrophysical disks” 58 1031–1058 (2015)
B.M. Bolotovskii, S.N. Stolyarov “Current status of the electrodynamics of moving media (infinite media)” 17 875–895 (1975)
G.M. Strakhovskii, N.V. Kravtsov “Strong magnetic fields” 3 260–272 (1960)
V.P. Tychinskii “Microscopy of subwavelength structures” 39 1157–1167 (1996)
S.Yu. Karpov, S.N. Stolyarov “Propagation and transformation of electromagnetic waves in one-dimensional periodic structures” 36 (1) 1–22 (1993)
S.A. Gredeskul, V.D. Freilikher “Localization and wave propagation in randomly layered media” 33 (2) 134–146 (1990)
M.L. Ter-Mikhaelyan “High energy electromagnetic processes in amorphous and inhomogeneous media” 46 1231–1252 (2003)
A.V. Timofeev “Electromagnetic waves in a magnetized plasma near the critical surface” 47 555–582 (2004)
V.I. Klyatskin “Electromagnetic wave propagation in a randomly inhomogeneous medium as a problem in mathematical statistical physics” 47 169–186 (2004)
D.A. Kirzhnits “General properties of electromagnetic response functions” 30 575–587 (1987)
V.F. Kravchenko, A.A. Kuraev, A.K. Sinitsyn “Nonsynchronous interactions” 50 489–511 (2007)
A.V. Gurevich “Nonlinear effects in the ionosphere” 50 1091–1121 (2007)
A.P. Vinogradov, A.V. Dorofeenko et al “Surface states in photonic crystals” 53 243–256 (2010)
A.V. Dorofeenko, A.A. Zyablovsky et al “Light propagation in composite materials with gain layers” 55 1080–1097 (2012)

The list is formed automatically.