Eigenwaves in Sommerfeld–Goubau Line: Spectrum
- Authors: Smirnov Y.G.1, Smolkin E.Y.1
-
Affiliations:
- Department of Mathematics and Supercomputing
- Issue: Vol 39, No 8 (2018)
- Pages: 1130-1139
- Section: Article
- URL: https://journals.rcsi.science/1995-0802/article/view/203022
- DOI: https://doi.org/10.1134/S1995080218080103
- ID: 203022
Cite item
Abstract
The problem on normal waves in an inhomogeneous metal-dielectric waveguide structure is reduced to a boundary value problem for the longitudinal components of the electromagnetic field in Sobolev spaces. Nonhomogeneous filling and entering of spectral parameter in transmission conditions leads to necessity of special definition of solution of the problem. We formulate the definition of solution using variational relation. The variational problem is reduced to the study of an operator function. We investigate properties of the operators of the operator function needed for the analysis of its spectral properties. We prove theorem of discrete spectrum and theorem of localization of eigenvalues of the operator-function on complex plane.
About the authors
Yu. G. Smirnov
Department of Mathematics and Supercomputing
Author for correspondence.
Email: smirnovyug@mail.ru
Russian Federation, ul. Krasnaya 40, Penza, 440026
E. Yu. Smolkin
Department of Mathematics and Supercomputing
Email: smirnovyug@mail.ru
Russian Federation, ul. Krasnaya 40, Penza, 440026