On problems of applying the parabolic equation to diffraction by prolate bodies

Abstract

This paper continues the investigation of the authors devoted to the axially symmetric problem of short-wave diffraction by prolate bodies of revolution. The paper briefly presents an approach based on a two-scale asymptotic expansion of the Leontovich-Fock parabolic equation and related problems that accomany this expansion. In the case of a strongly elongated body (e.g., the major semiaxis of an ellipsoid of revolution exceeds the minor semiaxis by a factor of >30), the corresponding parabolic equation and all subsequent recurrence equations become singular. In the nonaxisymmetric case, problems arise related to the specific behavior of geodesic lines on the scatterer surface.