Investigation of the shortwave diffraction by elongated bodies of revolution requires a detailed consideration of matching of local asymptotics in the illuminated part of the Fock domain. In the paper, that task is solved by means of a straightforward construction of the reflected wave with the help of the ray method. The main problem on the way, which was judged by V. A. Fock as a rather complicated one, is the calculation of the eikonal and the geometric spreading in curvilinear coordinates used in the boundary layer method in the vicinity of the light-shadow zone. Bibliography: 9 titles.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 426, 2014, pp. 49–63.
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Kirpichnikova, N.Y., Popov, M.M. Merging of Asymptotics in the Illuminated Part of the Fock Domain. J Math Sci 214, 277–286 (2016). https://doi.org/10.1007/s10958-016-2777-2
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DOI: https://doi.org/10.1007/s10958-016-2777-2