Abstract
In the work the interaction of normal waves in a neighborhood of approach or intersection of dispersion curves is studied. An asymptotic expression for a normal wave is constructed by means of a certain class of special functions. In the case of intersection, these functions are well-known standard integrals (Airy, Pirsli, etc. integrals). It is shown that by means of these special functions it is possible to describe the solution in a neighborhood of a point of approach or intersection of any number of caustics.
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Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 104, pp. 217–227, 1981.
In conclusion, the author thanks I. A. Molotkov for fruitful discussions and remarks.
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Starkov, A.S. A degeneracy phenomenon and resonance phenomena in problems of wave propagation. J Math Sci 20, 1883–1890 (1982). https://doi.org/10.1007/BF01119373
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DOI: https://doi.org/10.1007/BF01119373