4 papers · 1 filter
Vertex Green's functions of a quarter-plane. Links between the functional equation, additive crossing and Lamé functions
Raphaël C. Assier, Andrey V. Shanin
In our previous work (Assier \& Shanin, QJMAM, 2019), we gave a new spectral formulation in two complex variables associated with the problem of plane-wave diffraction by a quarter…
On the asymptotic properties of a canonical diffraction integral
Raphael C. Assier, I. David Abrahams
We introduce and study a new canonical integral, denoted , depending on two complex parameters and . It arises from the canonical problem of wave d…
A surprising observation on the quarter-plane diffraction problem
Raphael C. Assier, I. David Abrahams
In this paper, we revisit Radlow's highly original attempt at a double Wiener-Hopf solution to the canonical problem of wave diffraction by a quarter-plane. Using a constructive ap…
Diffraction by a quarter-plane. Analytical continuation of spectral functions
R. C. Assier, A. V. Shanin
The problem of diffraction by a Dirichlet quarter-plane (a flat cone) in a 3D space is studied. The Wiener-Hopf equation for this case is derived and involves two unknown (spectral…