Mathematical Theory of Normal Waves in Radially Inhomogenous Dielectric Rod
- Authors: Smirnov Y.1, Smolkin E.1
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Affiliations:
- Department of Mathematics and Supercomputing
- Issue: Vol 40, No 10 (2019)
- Pages: 1711-1724
- Section: Article
- URL: https://journals.rcsi.science/1995-0802/article/view/205978
- DOI: https://doi.org/10.1134/S1995080219100251
- ID: 205978
Cite item
Abstract
The problem on normal waves in a radially inhomogeneous dielectric rod is considered. This problem is reduced to the boundary eigenvalue problem for longitudinal components of electromagnetic field in Sobolev spaces. To find the solution, we use the variational formulation of the problem. The variational problem is reduced to study of an operator-function. Discreteness of the spectrum is proved and distribution of the characteristic numbers of the operator-function on the complex plane is found.
About the authors
Yury Smirnov
Department of Mathematics and Supercomputing
Author for correspondence.
Email: smirnovyug@mail.ru
Russian Federation, Penza, 440026
Eugene Smolkin
Department of Mathematics and Supercomputing
Author for correspondence.
Email: e.g.smolkin@hotmail.com
Russian Federation, Penza, 440026