2 citations · 5 across the 5 of their papers we have counts for
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…
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…
Criteria for commutative factorization of a class of algebraic matrices
Andrey V. Shanin, Eugeny M. Doubravsky
The problem of matrix factorization motivated by diffraction or elasticity is studied. A powerful tool for analyzing its solutions is introduced, namely analytical continuation for…
An ODE--based approach to some Riemann--Hilbert problems motivated by wave diffraction
Andrey V. Shanin
A novel approach to Riemann--Hilbert problems of particular class is introduced. The approach is applicable to problems in which the multiplicative jump is set on a half-line. Such…