Diffraction by a quarter–plane. Analytical continuation of spectral functions. Issue 1 (31st December 2018)

• Record Type: Journal Article
• Authors: Assier, R C; Shanin, A V
• Is Part Of: Quarterly journal of mechanics and applied mathematics. Volume 72:Issue 1(2019:Feb.)
• Page Start: 51
• Page End: 86
• Publication Date: 2018-12-31
• Subjects: Mechanics -- Mathematics -- Periodicals; Applied mathematics -- Periodicals; 530.1
• DOI: 10.1093/qjmam/hby021
• Languages: English
• ISSNs: 0033-5614

Abstract

Summary: 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) functions depending on two complex variables. The aim of the present work is to construct an analytical continuation of these functions onto a well-described Riemann manifold and to study their behaviour and singularities on this manifold. In order to do so, integral formulae for analytical continuation of the spectral functions are derived and used. It is shown that the Wiener–Hopf problem can be reformulated using the concept of additive crossing of branch lines introduced in the article. Both the integral formulae and the additive crossing reformulation are novel and represent the main results of this work.