Diffraction by a Right-Angled No-Contrast Penetrable Wedge Revisited: A Double Wiener-Hopf Approach
Mathematical Physics
2022-05-27 v2 Analysis of PDEs
Complex Variables
math.MP
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.
Keywords
Cite
@article{arxiv.2112.03173,
title = {Diffraction by a Right-Angled No-Contrast Penetrable Wedge Revisited: A Double Wiener-Hopf Approach},
author = {Valentin D. Kunz and Raphael C. Assier},
journal= {arXiv preprint arXiv:2112.03173},
year = {2022}
}