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

TL;DR

This paper revisits Radlow's diffraction approach for a penetrable wedge using a double Wiener-Hopf method, clarifying the limitations of his ansatz and deriving a system of equations governing the problem.

Contribution

It provides a constructive derivation of Radlow's ansatz and demonstrates why it cannot be the exact solution, offering new insights into the diffraction problem.

Findings

Radlow's ansatz is not the true solution to the diffraction problem.

The double Wiener-Hopf equation reduces to a coupled system of two equations.

A compatibility condition governs the behavior of the unknown function.

Abstract

In this paper, we revisit Radlow's innovative approach to diffraction by a penetra ble 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.