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Classical nonlinear dynamics and chaos of rays in problems of wave propagation in inhomogeneous media

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We discuss the geometrical theory of wave propagation in regularly inhomogeneous waveguide media from the point of view of nonlinear Hamiltonian dynamics. We consider ray dynamics in waveguides with periodic longitudinal inhomogeneities, including the phenomenon of spatial nonlinear resonance of rays, which leads to the formation of an effective waveguide channel in the neighborhood of the ray in resonance with the periodic inhomogeneities. We consider different properties of spatially resonant rays: the optical path length and propagation velocity of a signal along rays trapped in a separate nonlinear resonance; the fractal properties of rays, such as the "devil's staircase" form of the dependence of the spatial oscillation frequency of the ray and the propagation time of a signal along the rays. The trajectory of sound rays in a model of the ocean with transverse flow is considered using the adiabatic invariant method and the transverse drift of a ray with respect to the main propagation direction of sound is described. We consider the conditions for dynamical chaos of rays in a waveguide with longitudinal periodic inhomogeneities. We examine the conditions for internal spatial nonlinear resonance and chaos of rays in waveguides with an irregular cross section and their effect on the propagation velocity of a signal. We study the connection between the structure of the wave front and the dynamics of rays in waveguide channels with regular inhomogeneities. Finally, we discuss the applicability of geometrical optics in waveguides under the conditions of nonlinear resonance and chaos of rays, and the relation between this problem and quantum chaos.

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Fulltext is also available at DOI: 10.1070/PU1991v034n08ABEH002461
PACS: 05.45.Df, 05.45.Mt, 43.20.Dk (all)
DOI: 10.1070/PU1991v034n08ABEH002461
URL: https://ufn.ru/en/articles/1991/8/a/
Citation: Abdullaev S S, Zaslavskii G M "Classical nonlinear dynamics and chaos of rays in problems of wave propagation in inhomogeneous media" Sov. Phys. Usp. 34 (8) 645–664 (1991)
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Оригинал: Абдуллаев С С, Заславский Г М «Классические нелинейная динамика и хаос лучей в задачах распространения волн в неоднородных средах» УФН 161 (8) 1–43 (1991); DOI: 10.3367/UFNr.0161.199108a.0001

References (77) Cited by (57) ↓ Similar articles (20)

  1. Virovlyansky A L Uspekhi Fizicheskikh Nauk 193 1010 (2023)
  2. [Virovlyansky A L Phys. Usp. 66 951 (2023)]
  3. Makarov D, Petrov P S SSRN Journal (2022)
  4. Makarov D V, Petrov P S Wave Motion 115 103084 (2022)
  5. Gradoni G, Panichi F, Turchetti G 31 (4) (2021)
  6. Korolenko P V Phys. Wave Phen. 28 313 (2020)
  7. Makarov D V Wave Motion 90 205 (2019)
  8. Bizyaev I A, Borisov A V, Mamaev I S Regul. Chaot. Dyn. 23 665 (2018)
  9. Prants S V Phys. Scr. 92 044002 (2017)
  10. Makarov D V, Kon’kov L E, Petrov P S Radiophys Quantum El 59 576 (2016)
  11. Prants S V Phys. Scr. 90 074054 (2015)
  12. Prants S V Eur. Phys. J. Spec. Top. 223 2723 (2014)
  13. Virovlyansky A L, Makarov D V, Prants S V Uspekhi Fizicheskikh Nauk 182 19 (2012)
  14. Virovlyansky A L, Kazarova A Yu, Lyubavin L Ya Radiophys Quantum El 54 334 (2011)
  15. Virovlyansky A L, Kazarova A Yu, Lyubavin L Ya 129 2851 (2011)
  16. Virovlyansky A L, Kazarova A Yu, Lyubavin L Ya Acoust. Phys. 56 317 (2010)
  17. Virovlyansky A L Nonlinear Physical Science Vol. Hamiltonian Chaos Beyond the KAM TheoryChaos in Ocean Acoustic Waveguide0 Chapter 6 (2010) p. 255
  18. Virovlyansky A L, Kazarova A Yu, Lyubavin L Ya 125 1362 (2009)
  19. Virovlyansky A L, Kazarova A Yu et al Acoust. Phys. 54 654 (2008)
  20. VIROVLYANSKY A L Int. J. Bifurcation Chaos 18 2693 (2008)
  21. Makarov D V, Kon’kov L E, Uleysky M Yu Acoust. Phys. 54 382 (2008)
  22. Virovlyansky A L, Kazarova A Yu, Lyubavin L Ya Acoust. Phys. 54 486 (2008)
  23. Virovlyansky A L, Kazarova A Yu, Lyubavin L Ya Acoust. Phys. 53 181 (2007)
  24. Smirnov I P, Khil’ko A A Radiophys Quantum Electron 50 181 (2007)
  25. Virovlyansky A L, Kazarova A Yu, Lyubavin L Ya 121 2542 (2007)
  26. Virovlyanskiĭ A L, Zaslavskiĭ G M Acoust. Phys. 53 282 (2007)
  27. Makarov D V, Uleyskiy M Yu Acoust. Phys. 53 495 (2007)
  28. Kon’kov L E, Makarov D V et al Phys. Rev. E 76 (5) (2007)
  29. Makarov D V, Uleysky M Yu et al Phys. Rev. E 73 (6) (2006)
  30. Virovlyansky A L Acoust. Phys. 51 71 (2005)
  31. Smirnov I P, Virovlyansky A L et al Phys. Rev. E 72 (2) (2005)
  32. Smirnov I P, Virovlyansky A L, Zaslavsky G M 117 1595 (2005)
  33. Virovlyansky A L Acoust. Phys. 51 271 (2005)
  34. Virovlyansky A L, Kazarova A Yu, Lyubavin L Ya Wave Motion 42 317 (2005)
  35. Beron-Vera F J, Brown M G 115 1068 (2004)
  36. Makarov D V, Uleysky M Yu, Prants S V 14 79 (2004)
  37. Beron-Vera F J, Brown M G et al 114 1226 (2003)
  38. Virovlyansky A L 113 2523 (2003)
  39. Iomin A, Bliokh Yu Communications In Nonlinear Science And Numerical Simulation 8 389 (2003)
  40. Brown M G, Colosi J A et al 113 2533 (2003)
  41. Makarov D V, Uleysky M Yu, Prants S V Tech. Phys. Lett. 29 430 (2003)
  42. Smirnov I P, Virovlyansky A L, Zaslavsky G M 12 617 (2002)
  43. Smirnov I P, Virovlyansky A L, Zaslavsky G M Phys. Rev. E 64 (3) (2001)
  44. Virovlyanskii A L, Lyubavin L Ya, Stromkov A A Acoust. Phys. 47 517 (2001)
  45. Li X, Du G J. Opt. Soc. Am. B 18 318 (2001)
  46. Virovlyansky A L 108 84 (2000)
  47. Virovlyansky A L, Zaslavsky G M 10 211 (2000)
  48. Virovlyansky A L, Zaslavsky G M Phys. Rev. E 59 1656 (1999)
  49. Sundaram B, Zaslavsky G M 9 483 (1999)
  50. Bizarro J P S, Ferreira J S, Nakach R 6 1131 (1999)
  51. Zaslavsky G M, Abdullaev S S 7 182 (1997)
  52. Dubinov A E, Sadovoy S A Radiophys Quantum Electron 40 317 (1997)
  53. Peysson Y, Arslanbekov R et al 3 3668 (1996)
  54. Abdullaev S S 4 63 (1994)
  55. Chugurin V V, Erukhimov L M, Ryndyk E Yu Waves In Random Media 4 21 (1994)
  56. Erukhimov L M, Ryndyk E Yu, Chugurin V V Radiophys Quantum Electron 36 563 (1993)
  57. Zaslavsky G M, Strauss H R 2 469 (1992)
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