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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2008, Number 10, Pages 70–74 (Mi ivm1767)  
This article is cited in 6 scientific papers (total in 6 papers)

Brief communications

A nonlinear boundary eigenvalues problem for TM-polarized electromagnetic waves in a nonlinear layer

D. V. Valovik, Yu. G. Smirnov

Penza State University
Full-text PDF (159 kB) Citations (6)
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Abstract: We consider the propagation of TM-polarized electromagnetic waves in a nonlinear dielectric layer located between two linear media. The nonlinearity in the layer is described by the Kerr law. We reduce the problem to a nonlinear boundary eigenvalues problem for a system of ordinary differential equations. We obtain a dispersion relation and a first approximation for eigenvalues of the problem. We compare the results with those obtained for the case of a linear medium in the layer.
Keywords: dispersion relation, boundary value problem, Kerr nonlinearity.
Received: 25.12.2007
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2008, Volume 52, Issue 10, Pages 60–63
DOI: https://doi.org/10.3103/S1066369X08100083
Bibliographic databases:
Document Type: Article
UDC: 517.958
Language: Russian
Citation: D. V. Valovik, Yu. G. Smirnov, “A nonlinear boundary eigenvalues problem for TM-polarized electromagnetic waves in a nonlinear layer”, Izv. Vyssh. Uchebn. Zaved. Mat., 2008, no. 10, 70–74; Russian Math. (Iz. VUZ), 52:10 (2008), 60–63
Citation in format AMSBIB
\Bibitem{ValSmi08}
\by D.~V.~Valovik, Yu.~G.~Smirnov
\paper A nonlinear boundary eigenvalues problem for TM-polarized electromagnetic waves in a nonlinear layer
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2008
\issue 10
\pages 70--74
\mathnet{http://mi.mathnet.ru/ivm1767}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2530529}
\zmath{https://zbmath.org/?q=an:1177.78050}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2008
\vol 52
\issue 10
\pages 60--63
\crossref{https://doi.org/10.3103/S1066369X08100083}
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    • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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