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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.

Fulltext pdf (700 KB)
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
URL: https://ufn.ru/en/articles/1996/12/b/
A1996WE26100002
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

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

  1. Sternin B, Shatalov V Differential Equations on Complex Manifolds (Dordrecht, Boston: Academic Publ., 1994)
  2. Waterman P C J. Acoust. Soc. Am. 57 791 (1975); Masel R I, Merrill R P, Miller W H Phys. Rev. B 12 5545 (1975)
  3. Ramm A G J. Math. Phys. 23 1123 (1982)
  4. Hadamard J Le Probleme de Cauchy et les Équations aux Dérivées Partielles Linéaires Hyperboliques (Paris, 1932) [Translated into Russian (Moscow: Nauka, 1978)]
  5. Lewy H Math. Ann. 101 609 (1929)
  6. Davis Ph The Schwarz Functions and its Applications (Providence: Carus Mathematical Monographs, MAA, 1979)
  7. Khavinson D, Shapiro H S Research report TRITA-MAT-1989-36 (Stockholm: Royal Institute of Technology, 1989)
  8. Schwarz H A Monatsber. der KOnig Akad. der Wiss. zu Berlin 767 (1870)
  9. Shapiro H S The Schwarz Function and its Generalization to Higher Dimensions (New York: John Wiley, 1992)
  10. Khavinson D, Shapiro H S J. d’Analyse Mathématique 54 60 (1989)
  11. Vekua I N Novye Metody Resheniya Éllipticheskikh Uravneniî (Moscow, Leningrad: Gostekhizdat, 1948) [Translated into English Vekua I N New Methods for Solving Elliptic Equations (Amsterdam: North-Holland, 1967)]
  12. Lewy H Bull. Am. Math. Soc. 65 37 (1959)
  13. Sternin B Yu, Shatalov V E Geometriya i Analiz (Kemerovo: Kemerovo Univ. Press, 1991) p. 22
  14. Sternin B, Shatalov V Lect. Notes in Math. 1520 237 (1992)
  15. Kyurkchan A G, Sternin B Yu, Shatalov V E Radiotekh. Elektron. 37 777 (1992)
  16. Garabedian P J. Math. Mech. 9 241 (1960)
  17. Garabedian P Partial Differential Equations (New York, London, Sidney: John Wiley, 1964)
  18. Millar R F Lect. Notes in Math. 561 (1976)
  19. Millar R F IMA J. Appl. Math. 37 (2) 155 (1986)
  20. Sternin B, Shatalov V, Preprint 93 (Bonn: Max-Planck-Institut für Mathematik, 1994)
  21. Sternin B, Shatalov V, Preprint MPI/95-77 (Bonn: Max-Planck-Institut für Mathematik, 1995)
  22. Sternin B Yu, Shatalov V E Usp. Mat. Nauk 43 99 (1988)
  23. Sternin B Yu, Shatalov V E Dokl. Akad. Nauk SSSR 280 553 (1985) [Sov. Math. Dokl. 31 125 (1985)]
  24. Sternin B Yu, Shatalov V E Russian J. Math. Phys. 1 (2) 239 (1992)
  25. Sternin B Yu, Shatalov V E Mat. Zametki 54 90 (1993)
  26. Sternberg S Lectures on Differential Geometry (Englewood Cliffs, N.J.: Prentice Hall, Inc. 1964) [Translated into Russian (Moscow: Mir, 1970)]
  27. Leray J Bul. Soc. Math. de France 3 (87) 81 (1959)
  28. Pham F Introduction a L’Étude Topologique des Singularités de Landau (Paris: Gauthier-Villars, 1967)
  29. Sternin B Yu, Shatalov V E Lect. Notes in Math. 1453 109 (1990)
  30. Savina T V, Sternin B Yu, Shatalov V E Dokl. Akad. Nauk SSSR 322 48 (1992) [Sov. Math. Dokl. 45 (1) 42 (1992)]
  31. Savina T V, Sternin B Yu, Shatalov V E Radiotekh. Elektron. 38 229 (1993) [J. Commun. Electron. 38 132 (1993)]
  32. Colton D, Kress R Integral Equation Methods in Scattering Theory (New York: John Wiley, 1984) [Translated into Russian (Moscow: Mir, 1987)]
  33. Hönl H, Maue A, Wespfahl K Theorie der Beugung (Berlin - Heidelberg: Springer-Verlag, 1961) [Translated into Russian (Moscow: Mir, 1964)]
  34. Wilcox C H Comm. Pure and Appl. Math. 9 115 (1956)
  35. Kyurkchan A G Dokl. Akad. Nauk SSSR 319 854 (1991) [Sov. Phys. Dokl. 36 (8) 567 (1991)]
  36. Vekua I N Dokl. Akad. Nauk SSSR 90 715 (1953)
  37. Bohren C F, Huffman D R Absorption and Scattering of Light by Small Particles (New York: Wiley, 1983) [Translated into Russian (Moscow: Mir, 1986)]
  38. Kyurkchan A G Radiotekh. Elektron. 28 1275 (1983) [Radio Eng. & Electron. Physics 28 (7) 33 (1983)]
  39. Felsen L,’Marcuvitz N Radiation and Scattering of Waves (Englewood Cliffs, N.J.: Prentice-Hall, Inc., 1973) [Translated into Russian (Moscow: Mir, 1978)]
  40. Kyurkchan A G Dokl. Akad. Nauk SSSR 265 68 (1982) [Sov. Phys. Dokl. 27 (7) 577 (1982)]
  41. Kyurkchan A G Radiotekh. Elektron. 27 233 (1982) [Radio Eng. & Electron. Physics 27 (2) 35 (1982)]
  42. Kyurkchan A G Dokl. Akad Nauk (Russia) 336 728 (1994) [Phys. Dokl. 39 (8) 546 (1994)]
  43. Kyurkchan A G Radiotekh. Elektron. 28 1525 (1983) [Radio Eng. & Electron. Physics 28 (8) 53 (1983)]
  44. Kyurkchan A G, Sternin B Yu, Shatalov V E, in Trudy X Shkoly-Seminara po Difraktsii i Rasprostraneniyu Voln (Works of X School on Diffraction and Propagation of Waves, Moscow: NIIRF Publ., 1993) p. 268
  45. Hill N R, Celli V Phys. Rev. B 17 2478 (1978)
  46. Khurgin Ya I, Yakovlev V P Metody Teorii Tselykh Funktsiî v Radiofizike, Teorii Svyazi i Optike (Methods of Entire Functions Theory in Radiophysics, Communication Theory and Optics, Moscow: Fizmatgiz, 1962)
  47. Kyurkchan A G Radiotekh. Elektron. 31 1294 (1986) [Sov. J. Comm. Technol. Electron. 31 (11) 20 (1986)]
  48. Kyurkchan A G Dokl. Akad. Nauk SSSR 275 48 (1984) [Sov. Phys. Dokl. 29 (3) 180 (1984)]
  49. Fel’d Ya N, Bakhrakh L D Radiotekh. Elektron. 8 187 (1963)
  50. Kyurkchan A G, in Obratnye Zadachi. Materialy IX Vsesoyuznoî Shkoly po Difraktsii i Rasprostraneniyu Voln (Inverse Problems. Works of IX Allunion School on Kazan’, Kazan’: Kazan’ Aviation Institute Publ., 1988) p. 48
  51. Kyurkchan A G, Zimnov M Kh Radiotekh. Elektron. 33 53 (1988) [Sov. J. Comm. Technol. Electron. 33 (6) 47 (1988)]
  52. Kyurkchan A G Radiotekh. Elektron. 29 2129 (1984) [Sov. J. Commun. Technol. Electron. 30 48 (1985)]
  53. Kyurkchan A G Radiotekh. Elektron. 31 20 (1986) [Sov. J. Commun. Technol. Electron. 31 (5) 20 (1986)]
  54. Millar R F Radio Science 8 785 (1973)
  55. Kyurkchan A G Radiotekh. Elektron. 38 48 (1993) [J. Commun. Technol. Electron. 38 (6) 87 (1993)]
  56. Eremin Yu A, Sveshnikov A G Metod Diskretnykh Istochnikov v Zadachakh Élektromagnitnoî Difraktsii (Method of Auxiliary Sources in Electromagnetic Diffraction Problems, Moscow: Moscow State Univ. Publ., 1992)
  57. Boag A, Leviatan Y, Boag A IEEE Trans. Antennas and Propag. 41 1265 (1993)
  58. Kupradze V D Usp. Mat. Nauk 22 (2) 59 (1967)
  59. Kyurkchan A G, Kleev A I Radiotekh. Elektron. 41 162 (1996) [J. Commun. Technol. Electron. 41 (2) 146 (1996)]
  60. Kyurkchan A G Dokl. Akad. Nauk SSSR 325 273 (1992) [Sov. Phys. Dokl. 37 (7) 338 (1992)]
  61. Kyurkchan A G Dokl. Akad. Nauk (Russia) 339 600 (1994) [Phys. Dokl. 39 (12) 827 (1994)]
  62. Kyurkchan A G Dokl. Akad. Nauk (Russia) 348 603 (1996); 351 599 (1996) [Math. Dokl. 53 (3) 453 (1996)]
  63. Ufimtsev P Ya Metod Kraevykh Voln v Fizicheskoî Teorii Difraktsii (Method of Edge Waves in Physical Diffraction Theory, Moscow: Sovetskoe Radio, 1962)
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