ON SPECTRUM’S DISCRETE NATURE IN THE PROBLEM OF AZIMUTHAL SYMMETRICAL WAVES OF AN OPEN NONHOMOGENEOUS ANISOTROPIC WAVEGUIDE WITH LONGITUDINAL MAGNETIZATION 

Smirnov Yuriy Gennad'evich, Doctor of physical and mathematical sciences, professor, head of sub-department of mathematics and supercomputer modeling, Penza State University (40 Krasnaya street, Penza, Russia), mmm@pnzgu.ru
Smol'kin Evgeniy Yur'evich, Candidate of physical and mathematical sciences, research assistant, the research center “Supercomputer modeling in electrodynamics”, Penza State University (40 Krasnaya street, Penza, Russia), e.g.smolkin@hotmail.com
Snegur Maksim Olegovich, Student, Penza State University (40 Krasnaya street, Penza, Russia), snegur.max15@gmail.com

517.958;621.372.8

10.21685/2072-3040-2017-3-5

Background. The aim of the work is to research a spectrum of the problem of propogating electromagnetic waves of an anisotrpopic magnetic nonhomogeneous waveguiding structure.
Materials and methods. To find a solution we use variational problem formulation. The variational problem is reduced to studying of an operator-function that falls into nonlinear dependency from the spectral parameter. The article investigates properties of the operator-function necessary to analyze its spectral features.
Results. We have proved theorems on the spectrum’s discerete nature and on distributionof operator-function’s eigenvalues on a complex plance.
Conclusions. The suggested analytical method allows to prove the spectrum’sdiscrete nature in the problem of azimuthal symmetrical waves of an open nonhomogeneousanisotropic waveguide with longitudinal magnetization. Besides, thegiven method may be used in research of spectral properties of more complicatedwaveguiding structures.

problem of electromagnetic eave propagation, ferrite bar, Maxwell’s equation, differential equations, anisotropic nonhomogeneous waveguidingstructure, variational formulation, Sobolev’s spaces

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