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

Valery Yakhno; Ali Sevimlican

Applications of Mathematics (2011)

  • Volume: 56, Issue: 3, page 315-339
  • ISSN: 0862-7940

Abstract

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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 is reduced to an operator integral equation. After that the operator integral equation is solved by the method of successive approximations. Finally, a solution of the original initial value problem is found by the inverse Fourier transform.

How to cite

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Yakhno, Valery, and Sevimlican, Ali. "An analytic method for the initial value problem of the electric field system in vertical inhomogeneous anisotropic media." Applications of Mathematics 56.3 (2011): 315-339. <http://eudml.org/doc/116528>.

@article{Yakhno2011,
abstract = {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 is reduced to an operator integral equation. After that the operator integral equation is solved by the method of successive approximations. Finally, a solution of the original initial value problem is found by the inverse Fourier transform.},
author = {Yakhno, Valery, Sevimlican, Ali},
journal = {Applications of Mathematics},
keywords = {equations of electromagnetic theory; hyperbolic system of second order partial differential equations; initial value problem; analytical method; Fourier transform; equations of electromagnetic theory; hyperbolic system of second order partial differential equations; initial value problem; analytical method; Fourier transform},
language = {eng},
number = {3},
pages = {315-339},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {An analytic method for the initial value problem of the electric field system in vertical inhomogeneous anisotropic media},
url = {http://eudml.org/doc/116528},
volume = {56},
year = {2011},
}

TY - JOUR
AU - Yakhno, Valery
AU - Sevimlican, Ali
TI - An analytic method for the initial value problem of the electric field system in vertical inhomogeneous anisotropic media
JO - Applications of Mathematics
PY - 2011
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 56
IS - 3
SP - 315
EP - 339
AB - 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 is reduced to an operator integral equation. After that the operator integral equation is solved by the method of successive approximations. Finally, a solution of the original initial value problem is found by the inverse Fourier transform.
LA - eng
KW - equations of electromagnetic theory; hyperbolic system of second order partial differential equations; initial value problem; analytical method; Fourier transform; equations of electromagnetic theory; hyperbolic system of second order partial differential equations; initial value problem; analytical method; Fourier transform
UR - http://eudml.org/doc/116528
ER -

References

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