Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory
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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2020, Volume 176, Pages 34–49
DOI: https://doi.org/10.36535/0233-6723-2020-176-34-49 (Mi into585) 		 
Linearizable and nonlinearizable solutions in the nonlinear eigenvalue problem arising in the theory of electrodynamic waveguides filled with a nonlinear medium

D. V. Valovik, S. V. Tikhov

Penza State University
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DOI: https://doi.org/10.36535/0233-6723-2020-176-34-49
Abstract: In this paper, we consider a nonlinear eigenvalue problem on a segment, which describes the propagation of monochromatic (polarized) electromagnetic TM waves in a planar dielectric waveguide filled with a nonlinear medium. Results on the solvability of the problem and properties of the eigenvalues are obtained.
Keywords: Maxwell's equations, nonlinear eigenvalue problem, asymptotics of eigenvalues, planar dielectric waveguide, nonlinear permittivity.
Funding agency Grant number
Russian Science Foundation 18-71-10015
This work was supported by the Russian Science Foundation (project No. 18-71-10015).
Bibliographic databases:
Document Type: Article
UDC: 517.927.4; 517.988.57
MSC: 35P30, 34L20, 35Q61
Language: Russian
Citation: D. V. Valovik, S. V. Tikhov, “Linearizable and nonlinearizable solutions in the nonlinear eigenvalue problem arising in the theory of electrodynamic waveguides filled with a nonlinear medium”, Proceedings of the XVII All-Russian Youth School-Conference «Lobachevsky Readings-2018», November 23-28, 2018, Kazan. Part 2, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 176, VINITI, Moscow, 2020, 34–49
Citation in format AMSBIB
\Bibitem{ValTik20}
\by D.~V.~Valovik, S.~V.~Tikhov
\paper Linearizable and nonlinearizable solutions in the nonlinear eigenvalue problem arising in the theory of electrodynamic waveguides filled with a nonlinear medium
\inbook Proceedings of the XVII All-Russian Youth School-Conference «Lobachevsky Readings-2018»,
November 23-28, 2018, Kazan. Part 2
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2020
\vol 176
\pages 34--49
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into585}
\crossref{https://doi.org/10.36535/0233-6723-2020-176-34-49}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4150680}
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