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The Quarterly Journal of Mechanics and Applied Mathematics Advance Access originally published online on February 2, 2006
The Quarterly Journal of Mechanics and Applied Mathematics 2006 59(2):211-251; doi:10.1093/qjmam/hbj004
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Q. Jl Mech. Appl. Math, Vol. 59. No. 2 © The author 2006. Published by Oxford University Press; all rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

Electromagnetic scattering from an anisotropic impedance half-plane at oblique incidence: the exact solution

Y. A. Antipov{dagger}

( Department of Mathematics, Louisiana State University Baton Rouge LA 70803, USA )

V. V. Silvestrov{ddagger}

( Department of Mathematics, Chuvash State University Cheboksary 428015, Russia )

{dagger} Corresponding author antipov{at}math.lsu.edu

{ddagger} sil{at}chuvsu.ru

Scattering of a plane electromagnetic wave from an anisotropic impedance half-plane at skew incidence is considered. The two matrix surface impedances involved are assumed to be complex and different. The problem is solved in closed form. The boundary-value problem reduces to a system of two first-order difference equations with periodic coefficients subject to a symmetry condition. The main idea of the method developed is to convert the system of difference equations into a scalar Riemann–Hilbert problem on a finite contour of a hyperelliptic surface of genus 3. A constructive procedure for its solution and the solution of the associated Jacobi inversion problem is proposed and described in detail. Numerical results for the edge diffraction coefficients are reported.


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