Diffraction by a Right-Angled No-Contrast Penetrable Wedge Revisited: A Double Wiener-Hopf Approach

Abstract

In this paper, we revisit Radlow's innovative approach to diffraction by a penetrable wedge by means of a double Wiener-Hopf technique. We provide a constructive way of obtaining his ansatz and give yet another reason for why his ansatz cannot be the true solution to the diffraction problem at hand. The two-complex-variable Wiener-Hopf equation is reduced to a system of two equations, one of which contains Radlow's ansatz plus some correction term consisting of an explicitly known integral operator applied to a yet unknown function, whereas the other equation, the compatibility equation, governs the behaviour of this unknown function.

A contribution to the mathematical theory of diffraction. Part I: A note on double Fourier integrals

“…This work is part of the authors ongoing efforts to apply the theory of functions of several complex variables [6] to diffraction theory, see for instance [7][8][9][10][11][12][13][14]. A fundamental motivation behind the present work is that the methods developed here can be applied to the important canonical problem of diffraction by a quarter-plane studied in [8,9,11,[15][16][17][18][19][20] for instance.…”