Issues

 / 

1991

 / 

August

  

Reviews of topical problems


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

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.

Fulltext pdf (1.1 MB)
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)
BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks

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

Cited by (57) Similar articles (20) ↓

  1. A.L. Virovlyansky, D.V. Makarov, S.V. Prants “Ray and wave chaos in underwater acoustic waveguides55 18–46 (2012)
  2. G.M. Zaslavskii, B.V. Chirikov “Stochastic instability of non-linear oscillations14 549–568 (1972)
  3. G.P. Berman, A.R. Kolovskii “Quantum chaos in interactions of multilevel quantum systems with a coherent radiation field35 (4) 303–326 (1992)
  4. V.I. Tatarskii “The Wigner representation of quantum mechanics26 311–327 (1983)
  5. K.V. Koshel, S.V. Prants “Chaotic advection in the ocean49 1151–1178 (2006)
  6. G.M. Zaslavskii, R.Z. Sagdeev et alMinimal chaos, stochastic webs, and structures of quasicrystal symmetry31 887–915 (1988)
  7. P.V. Elyutin “The quantum chaos problem31 597–622 (1988)
  8. G.M. Zaslavskii “Statistics of energy spectra22 788–803 (1979)
  9. K.N. Alekseev, G.P. Berman et alDynamical chaos in magnetic systems35 (7) 572–590 (1992)
  10. D.A. Trunin “Pedagogical introduction to the Sachdev—Ye—Kitaev model and two-dimensional dilaton gravity64 219–252 (2021)
  11. V.V. Zosimov, L.M. Lyamshev “Fractals in wave processes38 347–384 (1995)
  12. L.M. Zelenyi, A.V. Milovanov “Fractal topology and strange kinetics: from percolation theory to problems in cosmic electrodynamics47 749–788 (2004)
  13. A.A. Makarov, A.L. Malinovsky, E.A. Ryabov “Intramolecular vibrational redistribution: from high-resolution spectra to real-time dynamics55 977–1007 (2012)
  14. G.M. Zaslavskii “Nonlinear waves and their interaction16 761–776 (1974)
  15. G.G. Kozlov, I.I. Ryzhov et alDevelopment of laser spectroscopy of spin noise67 (3) (2024)
  16. V.I. Klyatskin, D. Gurarie “Coherent phenomena in stochastic dynamical systems42 165 (1999)
  17. M.I. Rabinovich, A.L. Fabrikant, L.Sh. Tsimring “Finite-dimensional spatial disorder35 (8) 629–649 (1992)
  18. V.S. Anishchenko, T.E. Vadivasova et alStatistical properties of dynamical chaos48 151–166 (2005)
  19. A. Loskutov “Fascination of chaos53 1257–1280 (2010)
  20. A.V. Guglielmi, A.S. Potapov “Frequency-modulated ULF waves in near-Earth space64 452–467 (2021)

The list is formed automatically.

© 1918–2024 Uspekhi Fizicheskikh Nauk
Email: ufn@ufn.ru Editorial office contacts About the journal Terms and conditions