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Uspekhi Fizicheskikh Nauk, 1991, Volume 161, Number 8, Pages 1–43
DOI: https://doi.org/10.3367/UFNr.0161.199108a.0001
(Mi ufn7432)
 

This article is cited in 56 scientific papers (total in 56 papers)

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

S. S. Abdullaeva, G. M. Zaslavskyb

a Scientific Production Association "Cybernetics", Uzbekistan Academy of Sciences
b Space Research Institute, Moscow
Abstract: 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.
Received: September 24, 1990
Revised: May 16, 1991
English version:
Physics–Uspekhi, 1991, Volume 34, Issue 8
DOI: https://doi.org/10.1070/PU1991v034n08ABEH002461
Document Type: Article
UDC: 534.222
PACS: 05.45.Df, 05.45.Mt, 43.20.Dk
Language: Russian
Citation: S. S. Abdullaev, G. M. Zaslavsky, “Classical nonlinear dynamics and chaos of rays in problems of wave propagation in inhomogeneous media”, UFN, 161:8 (1991), 1–43
Citation in format AMSBIB
\Bibitem{AbdZas91}
\by S.~S.~Abdullaev, G.~M.~Zaslavsky
\paper Classical nonlinear dynamics and chaos of rays in problems of wave propagation in inhomogeneous media
\jour UFN
\yr 1991
\vol 161
\issue 8
\pages 1--43
\mathnet{http://mi.mathnet.ru/ufn7432}
\crossref{https://doi.org/10.3367/UFNr.0161.199108a.0001}
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  • This publication is cited in the following 56 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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