Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

A Genus-3 Riemann-Hilbert Problem and Diffraction of a Wave by Two Orthogonal Resistive Half-Planes

A Genus-3 Riemann-Hilbert Problem and Diffraction of a Wave by Two Orthogonal Resistive Half-Planes Diffraction of a plane electromagnetic wave (E-polarization) by two orthogonal electrically resistive half-planes is analyzed. The physical problem reduces to a Riemann-Hilbert problem in the real axis for four pairs of analytic functions $\Phi^+_j(\eta)(\eta\ \in\ \rm C^+)$$ and $$\Phi^-_j(\eta) = \Phi^+_j (-\eta)(\eta\ \in\ {\rm C}^-),j = 1,2,3,4,$ where ℂ+ and ℂ are the upper and lower half-planes. It is shown that the problem is equivalent to two scalar Riemann-Hilbert problems on a plane and a Riemann-Hilbert problem on a genus-3 hyperelliptic surface subject to a certain symmetry condition. A closed-form solution is derived in terms of singular integrals and the genus-3 Riemann Theta function. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Computational Methods and Function Theory Springer Journals

A Genus-3 Riemann-Hilbert Problem and Diffraction of a Wave by Two Orthogonal Resistive Half-Planes

Download PDF
24 pages

Loading next page...
 
/lp/springer-journals/a-genus-3-riemann-hilbert-problem-and-diffraction-of-a-wave-by-two-uRIeEv9LUd

References (23)

Publisher
Springer Journals
Copyright
Copyright © 2011 by Heldermann  Verlag
Subject
Mathematics; Analysis; Computational Mathematics and Numerical Analysis; Functions of a Complex Variable
ISSN
1617-9447
eISSN
2195-3724
DOI
10.1007/BF03321871
Publisher site
See Article on Publisher Site

Abstract

Diffraction of a plane electromagnetic wave (E-polarization) by two orthogonal electrically resistive half-planes is analyzed. The physical problem reduces to a Riemann-Hilbert problem in the real axis for four pairs of analytic functions $\Phi^+_j(\eta)(\eta\ \in\ \rm C^+)$$ and $$\Phi^-_j(\eta) = \Phi^+_j (-\eta)(\eta\ \in\ {\rm C}^-),j = 1,2,3,4,$ where ℂ+ and ℂ are the upper and lower half-planes. It is shown that the problem is equivalent to two scalar Riemann-Hilbert problems on a plane and a Riemann-Hilbert problem on a genus-3 hyperelliptic surface subject to a certain symmetry condition. A closed-form solution is derived in terms of singular integrals and the genus-3 Riemann Theta function.

Journal

Computational Methods and Function Theory – Springer Journals

Published: Apr 2, 2013

There are no references for this article.