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Zh. Vychisl. Mat. Mat. Fiz., 2013, Volume 53, Number 1, Pages 74–89 (Mi zvmmf9796)  

This article is cited in 5 scientific papers (total in 5 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

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.

DOI: https://doi.org/10.7868/S0044466913010158

Full text: PDF file (376 kB)
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English version:
Computational Mathematics and Mathematical Physics, 2013, 53:1, 78–92

Bibliographic databases:

UDC: 519.634
Received: 22.05.2012
Revised: 11.07.2012

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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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. D. V. Valovik, Yu. G. Smirnov, E. Yu. Smol'kin, “Nonlinear transmission eigenvalue problem describing TE wave propagation in two-layered cylindrical dielectric waveguides”, Comput. Math. Math. Phys., 53:7 (2013), 973–983  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    2. D. V. Valovik, E. Yu. Smol'kin, “Calculation of the propagation constants of inhomogeneous nonlinear double-layer circular cylindrical waveguide by means of the cauchy problem method”, J. Commun. Technol. Electron., 58:8 (2013), 762–769  crossref  mathscinet  isi  elib  scopus
    3. D. V. Valovik, E. A. Marennikova, Yu. G. Smirnov, “Nelineinaya zadacha sopryazheniya na sobstvennye znacheniya, opisyvayuschaya rasprostranenie elektromagnitnykh Te-voln v ploskom neodnorodnom nelineinom dielektricheskom volnovode”, Izvestiya vysshikh uchebnykh zavedenii. Povolzhskii region. Fiziko-matematicheskie nauki, 2013, no. 2(26), 50–63  elib
    4. I. S. Panyaev, D. G. Sannikov, “Dispersive properties of optical tm-type surface polaritons at a nonlinear semiconductor-nanocomposite (blig/ggg) interface”, J. Opt. Soc. Am. B-Opt. Phys., 33:2 (2016), 220–229  crossref  isi  elib  scopus
    5. E. Smolkin, Yu. Shestopalov, “Nonlinear Goubau line: analytical-numerical approaches and new propagation regimes”, J. Electromagn. Waves Appl., 31:8 (2017), 781–797  crossref  isi  scopus
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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