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An analytic method for the initial value problem of the electric field system in vertical inhomogeneous anisotropic media

Valery Yakhno;  Ali Sevimlican — 2011

Applications of Mathematics

The time-dependent system of partial differential equations of the second order describing the electric wave propagation in vertically inhomogeneous electrically and magnetically biaxial anisotropic media is considered. A new analytical method for solving an initial value problem for this system is the main object of the paper. This method consists in the following: the initial value problem is written in terms of Fourier images with respect to lateral space variables, then the resulting problem...

Computation of the fundamental solution of electrodynamics for anisotropic materials

Valery Yakhno;  Handan Yaslan;  Tatiana Yakhno — 2012

Open Mathematics

A new method for computation of the fundamental solution of electrodynamics for general anisotropic nondispersive materials is suggested. It consists of several steps: equations for each column of the fundamental matrix are reduced to a symmetric hyperbolic system; using the Fourier transform with respect to space variables and matrix transformations, formulae for Fourier images of the fundamental matrix columns are obtained; finally, the fundamental solution is computed by the inverse Fourier transform....

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