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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2013, Volume 53, Number 1, Pages 74–89
DOI: https://doi.org/10.7868/S0044466913010158 (Mi zvmmf9796) 		 
This article is cited in 12 scientific papers (total in 12 papers)

The method of cauchy problem for solving a nonlinear eigenvalue transmission problem for TM waves propagating in a layer with arbitrary nonlinearity

D. V. Valovik, E. V. Zarembo

Penza State University
Full-text PDF (376 kB) Citations (12)
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DOI: https://doi.org/10.7868/S0044466913010158
Abstract: The problem of plane monochromatic TM waves propagating in a layer with an arbitrary nonlinearity is considered. The layer is placed between two semi-infinite media. Surface waves propagating along the material interface are sought. The physical problem is reduced to solving a nonlinear eigenvalue transmission problem for a system of two ordinary differential equations. A theorem on the existence and localization of at least one eigenvalue is proven. On the basis of this theorem, a method for finding approximate eigenvalues of the considered problem is proposed. Numerical results for Kerr and saturation nonlinearities are presented as examples.
Key words: nonlinear eigenvalue transmission problem, Maxwell equations, Cauchy problem, approximate method for computation of eigenvalues.
Received: 22.05.2012
Revised: 11.07.2012
English version:
Computational Mathematics and Mathematical Physics, 2013, Volume 53, Issue 1, Pages 78–92
DOI: https://doi.org/10.1134/S0965542513010089
Bibliographic databases:
Document Type: Article
UDC: 519.634
Language: Russian
Citation: D. V. Valovik, E. V. Zarembo, “The method of cauchy problem for solving a nonlinear eigenvalue transmission problem for TM waves propagating in a layer with arbitrary nonlinearity”, Zh. Vychisl. Mat. Mat. Fiz., 53:1 (2013), 74–89; Comput. Math. Math. Phys., 53:1 (2013), 78–92
Citation in format AMSBIB
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    • This publication is cited in the following 12 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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