On Short-Wave Diffraction by a Strongly Elongated Body of Revolution

Abstract

This article deals with short-wave diffraction by a strongly elongated body of revolution (an axially symmetric problem). In this case, the classical method of the Leontovich–Fock parabolic equation (equations of the Schrödinger type, to be more precise) appears to be nonapplicable, because the corresponding recurrent system of equations loses its asymptotic nature, and the equations themselves, including the main parabolic equation, gain singularity in their coefficients. This paper introduces a new boundary layer in a neighborhood of the light-shadow boundary, which is determined by other scales than the Fock boundary layer. In the arising main parabolic equation, the variables are not separated, so it turns out to be impossible to construct a solution in analytic form. In this case we state a nonstationary scattering problem, where the arc length along the geodesic lines (meridians) plays the part of time, and the problem itself is resolved by numerical methods. Bibliography: 11 titles.