Abstract
In a thin waveguide with properties that vary along its course, the propagation of nonstationary normal waves in the presence of caustics for space-time rays is considered. The connection of the critical section of the waveguide with such caustics is determined. Uniform asymptotic formulas are obtained for the wave field in a multiray zone, and the passage into geometric rays outside a neighborhood of the caustics is traced.
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Literature cited
I. A. Molotkov and A. B. Plachenov, “Nonstationary normal waves in a thin, curved waveguide of variable cross section,” Zap. Nauchn. Sem. Leningr. Otd. Mat. Inst.,89, 210–218 (1979).
G. B. Whitham, Linear and Nonlinear Waves, Wiley (1974).
I. A. Molotkov, “The behavior of waveguide modes in a neighborhood of a critical section,” Zap. Nauchn. Sem. Leningr. Otd. Mat. Inst.,42, 181–188 (1974).
L. M. Brekhovskikh, Waves in Layered Media, Academic Press (1966).
Additional information
Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 99, pp. 127–137, 1980.
In conclusion, we note that the matrix machinery used in the present work is not connected with the special nature of the present problem and can always be applied when the initial Ansatz contains a collection of special functions which go over into one another under differentiation.
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Plachenov, A.B. Nonstationary normal waves in a thin, curved waveguide in a multiray zone (uniform asymptotics). J Math Sci 20, 2478–2486 (1982). https://doi.org/10.1007/BF01087295
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DOI: https://doi.org/10.1007/BF01087295