Abstract
In the paper a representation is obtained of the field of a point source in a waveguide with quadratic dependence of the index of refraction in the form of a sum of normal, geometrical-optics waves and a remainder. Sufficient conditions on the number of separate normal and geometrical-optics waves are found. The remainder is expressed by a simple formula.
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Literature cited
L. M. Brekhovskikh, Acoustics of the Ocean [in Russian], Nauka, Moscow (1974).
V. S. Buldyrev, “The field of a point source in a waveguide,” Tr. Mosk. Inst. Akad. Nauk,115, 78–102 (1971).
D. Ludwig, “Diffraction by a circular cavity,” J. Math. Phys.,11, No. 5, 1617–1630 (1970).
V. M. Kudryashov, “A geometric-wave method of computing acoustic fields in a waveguide,” Akust. Zh.,22, No. 5, 724–728 (1976).
V. B. Filippov, “Short-wave asymptotics of the current and the direction diagram for the problem of diffraction by nonplanar screens,” in: Theory of the Diffraction and Propagation of Waves. Seventh All-Union Symposium on the Diffraction and Propagation of Waves [in Russian], Moscow, Vol. 1 (1977), pp. 47–50.
Additional information
Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 99, pp. 146–156, 1980.
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Filippov, V.B. A method of calculating the field of a point source in a waveguide. J Math Sci 20, 2492–2499 (1982). https://doi.org/10.1007/BF01087297
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DOI: https://doi.org/10.1007/BF01087297