Abstract
The shortwave asymptotics of the Green function for a segment is investigated in the case of the Neumann boundary condition. In the shadow zone and the light zone terms describing the diffracted waves issuing from the end points of the segment are separated out from the solution in the form of a contour integral. The corresponding single integrals are then reduced to expressions coinciding with the formulas of the geometric theory of diffraction. It is here found, that the primary diffracted waves are described by series of residues having the same order with respect to the large parameter of the problem; for the series describing multiple diffracted waves it suffices to restrict attention to a single residue.
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Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 78, pp. 60–89, 1978.
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Grigor'eva, N.S. Diffraction of short waves by a segment. J Math Sci 22, 1036–1056 (1983). https://doi.org/10.1007/BF01305286
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DOI: https://doi.org/10.1007/BF01305286