The Wiener--Hopf Technique for Impenetrable Wedges Having Arbitrary Aperture Angle

Abstract

Diffraction by impenetrable wedges having arbitrary aperture angle is studied by means of the Wiener--Hopf (W-H) technique. A system of functional equations called generalized Wiener--Hopf equations (GWHE) is obtained. Only for certain values of the aperture angle are these equations recognizable as standard or classical Wiener--Hopf equations (CWHE). However, in all cases a mapping is found that reduces the GWHE to CWHE. It means that the diffraction by an impenetrable wedge always reduces to a standard W-H factorization. The solution for the diffraction by a wedge with given face impedances (the Malyuzhinets problem) is obtained in closed form by an explicit factorization of the kernel.