# Vector functional-difference equation in electromagnetic scattering

@article{Antipov2004VectorFE, title={Vector functional-difference equation in electromagnetic scattering}, author={Yuri A. Antipov and V. V. Silvestrov}, journal={Ima Journal of Applied Mathematics}, year={2004}, volume={69}, pages={27-69} }

A vector functional-difference equation of the first order with a special matrix coefficient is analysed. It is shown how it can be converted into a Riemann-Hilbert boundary-value problem on a union of two segments on a hyper-elliptic surface. The genus of the surface is defined by the number of zeros and poles of odd order of a characteristic function in a strip. An even solution of a symmetric Riemann-Hilbert problem is also constructed. This is a key step in the procedure for diffraction…

## 10 Citations

### Method of Hyperelliptic Surfaces for Vector Functional-Difference Equations

- Mathematics
- 2003

A vector functional-difference equation of the first order with a special matrix coeffcient is analysed. It is shown how it can be converted into a Riemann-Hilbert boundary-value problem on a union…

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An analytical method for scalar second-order functional-difference equations with meromorphic periodic coefficients is proposed. The technique involves reformulating the equation as a vector…

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

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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…

### The Prandtl integrodifferential equation and the contact problem for a piecewise homogeneous plate

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### The Problem of Linear Conjugation on a Closed Riemann Surface

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- 2008

Abstract.In this paper, we present a general solution of the scalar Riemann problem on a closed Riemann surface in the case of a compound contour in the class of piecewise meromorphic functions…

### On separation of a layer from the half-plane: Elastic fixation conditions for a plate equivalent to the layer

- Engineering
- 2015

The solution of the homogeneous problem on a half-infinite crack passing along the interface between a thin layer and an elastic half-plane made of materials with distinct properties is obtained and…

### Necessary condition of commutative factorization of algebraic matrices

- MathematicsProceedings of the International Conference Days on Diffraction-2005
- 2005

The problem of factorization of an algebraical matrix is studied. Analytical continuation formulae for solutions are derived. Necessary conditions for commutative factorization are found; a link with…

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