Mathematics

The method of operator functions in the problem of normal waves of an anisotropic screened waveguide of arbitrary section

E. Yu. Smol'kin, M. O. Snegur

Penza State University, Penza

Abstract: Background. The goal of the work is to study the spectral properties of the problem of normal waves of an anisotropic magnetic wave-leading structure. Materials and methods. To find the solution, a variational formulation of the problem is used. The problem is reduced to analyzing an operator function that is nonlinearly dependent on the propagation constant. The properties of the operator-function necessary to analyze the properties of the spectrum of the problem are investigated. Results. Results were obtained regarding the localization of the characteristic numbers of the operator function on the complex plane. The question of double completeness of the system of eigenfunctions and associated vectors with a finite defect is considered. Conclusion. The proposed analytical method allows one to prove the discreteness of the spectrum in the problem of symmetric azimuthal waves of a closed inhomogeneous anisotropic waveguide with longitudinal magnetization. In addition, this method can be used to study the spectral properties of more complex wave-leading structures.

Keywords: Maxwell's equation, anisotropic inhomogeneous wave-leading structure, variational formulation, Sobolev spaces, double completeness with Keldysh defect.

UDC: 517.927.2:621.372.8

DOI: 10.21685/2072-3040-2018-3-5