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BSU bulletin. Mathematics, Informatics

Bibliographic description:
Shirapov D. S.
,
Itigilov G. B.
,
Yumov I. B.
,
Anakhin V. D.
,
Dambaev Z. G.
DIRICHLET PROBLEM FOR HELMHOLTZ EQUATIONS IN GYROTROPIC ELLIPTICAL REGION WITH LONGITUDINAL MAGNETIZATION // BSU bulletin. Mathematics, Informatics. - 2019. №3. . - С. 17-31.
Title:
DIRICHLET PROBLEM FOR HELMHOLTZ EQUATIONS IN GYROTROPIC ELLIPTICAL REGION WITH LONGITUDINAL MAGNETIZATION
Financing:
Codes:
DOI: 10.18101/2304-5728-2019-3-17-31UDK: 517.95
Annotation:
We have formulated and solved the Dirichlet problem for Helmholtz equations of electromagnetic waves, propagating in an elliptical cylinder filled with longitu- dinally magnetized ferrite which is described by a second-rank tensor. It is assumed that the cylinder has an infinitely conductive wall. To solve the boundary value problem of Helmholtz equations for longitudinal components of electromagnetic waves, we have used the method of shortening the initial differential equation and the method of variables separation. The solution of the above boundary value prob- lem in elliptic coordinates is associated with the use of even and odd ordinary and modified Mathieu functions of the first kind. Using the results obtained, we have determined all the components of electromagnetic waves for even and odd solu- tions. Applying the Dirichlet condition to the components of electromagnetic waves and solving the system of linear homogeneous algebraic equations, we have ob- tained dispersion equations. The found dispersion equations of electromagnetic waves are of great practical importance and allow studying the propagation of hy- brid waves in this region.
Keywords:
elliptical cylinder; ferrite; Dirichlet problem; Helmholtz equation; electromagnetic wave; longitudinal magnetization; gyrotropic region; transverse com- ponents of the electromagnetic field; Mathieu functions; dispersion equation.
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