Abstract
The behavior of rays is studied in a neighborhood of boundary points where the curvature has a zero of multiplicity one (an inflection point) and multiplicity two (a flat point of a boundary which is concave from the side of the wave field). The rays considered away from the flat point of the boundary are connected with a whispering gallery wave incident on this point, and they are constructed on the basis of the known asymptotics of this wave. The results are represented in figures obtained with the help of the computer.
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Literature cited
M. M. Popov and I. Pshenchik, “Numerical solution of the problem of whispering gallery waves in a neighborhood of a simple zero of the effective curvature of the boundary,” Zap. Nauchn. Sem. Leningr. Otd. Mat. Inst.,62, 207–219 (1976).
M. M. Popov and I. Pshenchik, “Whispering gallery waves in a neighborhood of a flat point of a concave boundary,” Zap. Nauchn. Sem. Leningr. Otd. Mat. Inst.,78, 203–210 (1978).
M. M. Popov, “The wave field in the caustic shadow in a neighborhood of an inflection point of the boundary,” Zap. Nauchn. Sem. Leningr. Otd. Mat. Inst.,89, 246–260 (1979).
M. M. Popov, “On the problem of whispering gallery waves in a neighborhood of a simple zero of the effective curvature of the boundary,” Zap. Nauchn. Sem. Leningr. Otd. Mat. Inst.,62, 197–206 (1976).
Additional information
Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 104, pp. 146–155, 1981.
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Lanin, A.I., Popov, M.M. Ray dynamics in a neighborhood of flat points of the boundary. J Math Sci 20, 1840–1845 (1982). https://doi.org/10.1007/BF01119368
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DOI: https://doi.org/10.1007/BF01119368