Radiophysics and Quantum Electronics

, Volume 32, Issue 12, pp 1063–1081 | Cite as

Gaussian summation method (review)

  • V. M. Babich
  • M. M. Popov
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Literature Cited

  1. 1.
    O. Fresnel, Selected Works in Optics [Russian translation], Gostekhizdat, Moscow (1955).Google Scholar
  2. 2.
    L. D. Landau and E. M. Lifshits, Field Theory [in Russian], Nauka, Moscow (1973).Google Scholar
  3. 3.
    V. A. Fok, Problems in the Diffraction and Propagation of Electromagnetic Waves [in Russian], Sov. Radio, Moscow (1970).Google Scholar
  4. 4.
    V. M. Babich and V. S. Buldyrev, Asymptotic Methods in Problems of Short-Wave Diffraction [in Russian], Nauka, Moscow (1972).Google Scholar
  5. 5.
    Yu. A. Kravtsov, Izv. Vyssh. Uchebn. Zaved., Radiofiz.,7, No. 4, 664 (1964).Google Scholar
  6. 6.
    D. Ludwig, Commun. Pure Appl. Math.,19, No. 2, 215 (1966).Google Scholar
  7. 7.
    J. N. L. Connor, P. R. Curtis, and D. Farrelly, J. Phys. A: Math. Gen.,17, No. 2, 283 (1984).Google Scholar
  8. 8.
    L. Levey and L. B. Felsen, Radio Sci.,4, No. 10, 959 (1969).Google Scholar
  9. 9.
    Yu. I. Orlov, Radiotekh. Elektron.,21, No. 4, 730 (1976).Google Scholar
  10. 10.
    Yu. A. Kravtsov and Yu. I. Orlov, Usp. Fiz. Nauk,141, No. 4, 591 (1983).Google Scholar
  11. 11.
    V. P. Maslov, The Theory of Perturbations and Asymtotic Methods [in Russian], Gos. un-t., Moscow (1965).Google Scholar
  12. 12.
    V. P. Maslov and M. V. Fedoryuk, The Quasiclassic Approximation for the Equations of Quantum Mechanics [in Russian], Nauka, Moscow (1976).Google Scholar
  13. 13.
    B. R. Vainberg, Asymptotic Methods in the Equations of Mathematical Physics [in Russian], Gos. un-t, Moscow (1982).Google Scholar
  14. 14.
    D. S. Lukin and E. A. Palkin, The Numerical Canonic Method in Problems of the Diffraction and Propagation of Electromagnetic Waves in Nonuniform Media [in Russian], MFTI, Moscow (1982).Google Scholar
  15. 15.
    D. S. Lukin, E. B. Ipatov, and E. A. Palkin, Interdisciplinary Handbook [in Russian], MFTI, Moscow (1982), p. 21.Google Scholar
  16. 16.
    D. Ludwig, Commun. Pure Appl. Math.,20, No. 1, 103 (1967).Google Scholar
  17. 17.
    Yu. I. Orlov, Trudy MÉI, No. 119, 82 (1972).Google Scholar
  18. 18.
    Yu. I. Orlov, Izv. Vyssh. Uchebn. Zaved. Radiofiz.,17, No. 7, 1035 (1974).Google Scholar
  19. 19.
    Yu. I. Orlov and A. V. Demin, in: Investigating the Conditions of Radiowave Propagation [in Russian], IZMIRAN, Moscow (1983), p. 48.Google Scholar
  20. 20.
    A. V. Demin and I. L. Dudyreva, in: Abstracts of the 14th All-Union Conference on the Propagation of Radio Waves, Nauka, Moscow, Chap. 1, (1984), p. 251.Google Scholar
  21. 21.
    V. B. Avdeev, A. V. Demin, Yu. A. Kravtsov, M. V. Tinin, and A. P. Yarygin, in: Acoustic Waves in the Ocean, L. M. Brekhovskii and I. B. Andreeva (eds.) [in Russian], Nauka, Moscow (1987).Google Scholar
  22. 22.
    V. M. Babich and T. F. Pankratova, in: Problems of Mathematical Physics [in Russian], Gos. un-t, Leningrad No. 6, (1973), p. 9.Google Scholar
  23. 23.
    M. M. Popov, Zap. Nauchn. Seminarov Leningr. otd. Matem. in-ta Akad. Nauk SSSR,104, 195 (1981).Google Scholar
  24. 24.
    L. A. Vainshtein, Open Resonators and Open Waveguides [in Russian], Sov. Radio, Moscow (1966).Google Scholar
  25. 25.
    V. P. Maslov, The Complex WKB Method in Nonlinear Equations [in Russian], Nauka, Moscow (1977).Google Scholar
  26. 26.
    V. M. Babich and V. V. Ulin, Zap. nauchn. seminarov Leningr. otd. Matem. in-ta Akad. Nauk SSSR,117, 5 (1981).Google Scholar
  27. 27.
    V. E. Nomofilov, Zap. Nauchn. Seminarov Leningr. otd. Matem. in-ta Akad. Nauk SSSR,104, 170 (1981).Google Scholar
  28. 28.
    M. M. Popov, Vestnik Leningr. un-ta, No. 22, 43 (1969).Google Scholar
  29. 29.
    T. F. Pankratova, Zap. nauchn. seminarov Leningr. otd. Matem. in-ta Akad. Nauk SSSR,15, 122 (1969).Google Scholar
  30. 30.
    N. Ya. Kirpichnikova, Trudy MIAN SSSR,115, 103 (1971).Google Scholar
  31. 31.
    N. Ya. Kirpichnikova, Zap. Nauchn. Seminarov Leningr. otd. Matem. in-ta Akad. Nauk SSSR,15, 91 (1969).Google Scholar
  32. 32.
    N. Ya. Kirpichnikova, Zap. Nauchn. Seminarov Leningr. otd. Matem. in-ta Akad. Nauk SSSR,115, 114 (1971).Google Scholar
  33. 33.
    V. Cerveny and I. Psencik, Geophys. J. R. Astr. Soc.,72, 417 (1983).Google Scholar
  34. 34.
    K. Yomogida, Geophys. J. R. Astr. Soc.,82, 511 (1985).Google Scholar
  35. 35.
    J. A. Arnaud and H. Kogelnik, Appl. Optics,8, 1687 (1969).Google Scholar
  36. 36.
    G. A. Deschamps, Electr. Lett.,7, 684 (1971).Google Scholar
  37. 37.
    J. B. Keller and W. Streifer, J. Opt. Soc. Am.,61, 40 (1971).Google Scholar
  38. 38.
    L. B. Felsen, Geophys. J. R. Astr. Soc.,79, 77 (1984).Google Scholar
  39. 39.
    M. M. Popov, Izv. Akad. Nauk SSSR, Ser. Fiz. Zemli, No. 9, 39 (1983).Google Scholar
  40. 40.
    M. I. Yavor, Vestn. Leningr. un-ta, No. 4, 84 (1983).Google Scholar
  41. 41.
    L. Klimes, Geophys. J. R. Astr. Soc.,79, 105 (1984).Google Scholar
  42. 42.
    A. P. Kachalov, M. M. Popov, and I. Pshenchik, Zap. Nauchn. Seminarov Leningr. otd. Matem. in-ta Akad. Nauk SSSR,128, 65 (1983).Google Scholar
  43. 43.
    A. P. Kachalov and M. M. Popov, in: Mathematical Problems of Geophysics: Simulation, Research, and Interpretation [in Russian], Novosibirsk (1985), p. 3.Google Scholar
  44. 44.
    M. M. Popov, I. Psencik, and V. Cerveny, EGS Meeting, Budapest (1980).Google Scholar
  45. 45.
    V. Cerveny, M. M. Popov, and I. Psencik, Geophys. J. R. Astr. Soc.,70, 109 (1982).Google Scholar
  46. 46.
    A. P. Kachalov and M. M. Popov, Dokl. Akad. Nauk SSSR,258, No. 5, 1097 (1981).Google Scholar
  47. 47.
    M. M. Popov and A. P. Kachalov, Abstracts of 8th All-Union Symposium on Wave Diffraction and Propagation, Moscow (1981), Vol. 2, p. 253.Google Scholar
  48. 48.
    V. A. Eremenko and Yu. A. Cherkashin, in: Abstracts of 8th All-Union Symposium on Wave Diffraction and Propagation, Moscow (1981), Vol. 2, p,. 257.Google Scholar
  49. 49.
    V. É. Grikurov and M. M. Popov, Izv. Akad. Nauk SSSR, Ser. Fiz. Zemli, No. 8, 101 (1983).Google Scholar
  50. 50.
    V. E. Grikurov and M. M. Popov, Wave Motion,5, 225 (1983).Google Scholar
  51. 51.
    A. P. Kachalov and M. M. Popov, Preprint No. P-9-82, Leningr. otd. Matem. in-ta. Akad. Nauk SSSR (1982).Google Scholar
  52. 52.
    A. P. Katchalov and M. M. Popov, Geophys. J. R. Astr. Soc.,81, 205 (1985).Google Scholar
  53. 53.
    V. Cerveny, J. Geophys.,58, 44 (1985).Google Scholar
  54. 54.
    V. S. Buldyrev, Trudy MIAN SSSR,115, 78 (1971).Google Scholar
  55. 55.
    V. S. Buldyrev, in: Problems in the Dynamic Theory of Seismic-Wave Propagation [in Russian], Vol. 14, p. 84.Google Scholar
  56. 56.
    M. B. Porter and H. P. Bucker, J. Acoust. Soc. Am.,82, No. 4, 1349 (1987).Google Scholar
  57. 57.
    A. S. Kryukovskii, D. S. Lukin, and E. A. Palkin, Izv. Vyssh. Uchebn. Zaved., Radiofiz.,29, No. 1, 79 (1986).Google Scholar
  58. 58.
    B. É. Grikurov, E. B. Ipatov, A. S. Kryukovskii, D. S. Lukin, and E. A. Palkin, Interdisciplinary Handbook on the Diffraction and Propagation of Waves in Nonuniform Media [in Russian], Moscow (1987).Google Scholar
  59. 59.
    A. N. Norris, J. Opt. Soc. Am. A,3, 2005 (1986).Google Scholar
  60. 60.
    I. T. Lu, L. B. Felsen, and Y. Z. Ruan, Geophys. J. R. Astr. Soc.,89, 915 (1987).Google Scholar
  61. 61.
    B. S. White, A. Norris, A. Bayliss, and R. Burridge, Geophys. J. R. Astr. Soc.,89, 579 (1987).Google Scholar
  62. 62.
    A. I. Lanin and M. M. Popov, Zap. Nauchn. Seminarov Leningr. otd. Matem. in-ta Akad. Nauk SSSR,148, 116 (1985).Google Scholar
  63. 63.
    R. Wu, Geophys. J. R. Astr. Soc.,83, 93 (1985).Google Scholar
  64. 64.
    V. M. Babich, V. S. Buldyrev, and I. A. Molotkov, The Space-Time Radiant Method. Linear and Nonlinear Waves [in Russian], Gos. in-t, Leningrad (1985).Google Scholar
  65. 65.
    V. I. Smirnov, A Course in Higher Mathematics [in Russian], Fizmatgiz, Moscow, Vol. 4, (1958).Google Scholar
  66. 66.
    A. P. Kachalov, Zap. Nauchn. Seminarov Leningr. otd. Matem. in-ta Akad. Nauk SSSR,140, 73 (1984).Google Scholar
  67. 67.
    Ya. V. Kurylev, Zap. Nauchn. Seminarov Leningr. otd. Matem. in-ta Akad. Nauk SSSR,148, 104 (1985).Google Scholar
  68. 68.
    A. N. Norris, B. S. White, and Schrieffer, Proc. R. Soc. London A,412, 93 (1987).Google Scholar
  69. 69.
    A. N. Norris, Wave Motion,9, No. 6, 509 (1987).Google Scholar
  70. 70.
    N. Ya. Kirpichnikova and M. M. Popov, Zap. Nauchn. Seminarov Leningr. otd. Matem. in-ta Akad. Nauk SSSR,128, 72 (1983).Google Scholar
  71. 71.
    A. P. Kiselev, Izv. Vyssh. Uchebn. Zaved., Radiofiz.,26, No. 8, 1014 (1983).Google Scholar
  72. 72.
    M. M. Popov, Preprint No. P-6-86, Leningr. Otd. Matem. in-ta, Akad. Nauk SSSR, Leningrad (1986).Google Scholar
  73. 73.
    M. M. Popov, Zap. Nauchn. Seminarov Leningr. otd. Matem. in-ta Akad. Nauk SSSR,165, 143 (1987).Google Scholar
  74. 74.
    Yu. L. Gazaryan, in: Problems in the Dynamic Theory of Seismic-Wave Propagation [in Russian], Gos. in-t, Leningrad, Vol. 5 (1961), p. 90.Google Scholar
  75. 75.
    C. H. Chapman, Geophys. J. R. Astr. Soc.,54, 481 (1978).Google Scholar
  76. 76.
    C. H. Chapman and R. Drummond, Bull. Seismol. Soc. Am.,72, S277 (1982).Google Scholar
  77. 77.
    C. H. Chapman, J. Geophys.,58, 27 (1985).Google Scholar
  78. 78.
    A. P. Kachalov, Zap. Nauchn. Seminarov Leningr. otd. Matem. in-ta Akad. Nauk SSSR,148, 89 (1985).Google Scholar
  79. 79.
    A. P. Kachalov and M. M. Popov, Zap. Nauchn. Seminarov Leningr. otd. Matem. in-ta Akad Nauk SSSR,156, 73 (1986).Google Scholar
  80. 80.
    A. P. Katchalov and M. M. Popov, Geophys. J.,93, 465 (1988).Google Scholar
  81. 81.
    R. Madariaga, Geophys. J. R. Astr. Soc.,79, 589 (1984).Google Scholar
  82. 82.
    B. É. Grikurov and A. P. Kiselev, Izv. Vyssh. Uchebn. Zaved., Radiofiz.,29, No. 3, 307 (1986).Google Scholar
  83. 83.
    A. Ben-Menahem and W. B. Beydoun, Geophys. J. R. Astr. Soc.,82, 207 (1985).Google Scholar
  84. 84.
    W. B. Beydoun and A. Ben-Menahem, Geophys. J. R. Astr. Soc.,82, 235 (1985).Google Scholar
  85. 85.
    M. A. Lyalinov, Article No. 2878-B88, registered at VINITI, April 15, 1988.Google Scholar
  86. 86.
    J. M. Arnold, Radio Science,17, No. 5, 1181 (1982).Google Scholar
  87. 87.
    J. M. Arnold, IEE Proc.,133, Pt. J. No. 2, 165 (1986).Google Scholar
  88. 88.
    Yu. A. Kravtsov, Izv. Vyssh. Uchebn. Zaved., Radiofiz.,10, No. 9–10, 1283 (1967).Google Scholar

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© Plenum Publishing Corporation 1990

Authors and Affiliations

  • V. M. Babich
  • M. M. Popov

There are no affiliations available

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