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Zh. Vychisl. Mat. Mat. Fiz., 2013, Volume 53, Number 7, Pages 1150–1161 (Mi zvmmf9828)  

This article is cited in 6 scientific papers (total in 6 papers)

Nonlinear transmission eigenvalue problem describing TE wave propagation in two-layered cylindrical dielectric waveguides

D. V. Valovik, Yu. G. Smirnov, E. Yu. Smol'kin

Penza State University

Abstract: The paper is concerned with propagation of surface TE waves in a circular nonhomogeneous two-layered dielectric waveguide filled with a Kerr nonlinear medium. The problem is reduced to the analysis of a nonlinear integral equation with a kernel in the form of a Green’s function. The existence of propagating TE waves is proved using the contraction mapping method. For the numerical solution of the problem, two methods are proposed: an iterative algorithm (whose convergence is proved) and a method based on solving an auxiliary Cauchy problem (the shooting method). The existence of roots of the dispersion equation (propagation constants of the waveguide) is proved. Conditions under which k waves can propagate are obtained, and regions of localization of the corresponding propagation constants are found.

Key words: propagation of surface TE waves, nonhomogeneous two-layered dielectric waveguide, nonlinear eigenvalue problem, Green’s function, nonlinear integral equation, iterative method for numerical solution.

DOI: https://doi.org/10.7868/S004446691307020X

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English version:
Computational Mathematics and Mathematical Physics, 2013, 53:7, 973–983

Bibliographic databases:

UDC: 519.63,517.958:535.4
Received: 11.02.2013

Citation: D. V. Valovik, Yu. G. Smirnov, E. Yu. Smol'kin, “Nonlinear transmission eigenvalue problem describing TE wave propagation in two-layered cylindrical dielectric waveguides”, Zh. Vychisl. Mat. Mat. Fiz., 53:7 (2013), 1150–1161; Comput. Math. Math. Phys., 53:7 (2013), 973–983

Citation in format AMSBIB
\by D.~V.~Valovik, Yu.~G.~Smirnov, E.~Yu.~Smol'kin
\paper Nonlinear transmission eigenvalue problem describing TE wave propagation in two-layered cylindrical dielectric waveguides
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2013
\vol 53
\issue 7
\pages 1150--1161
\jour Comput. Math. Math. Phys.
\yr 2013
\vol 53
\issue 7
\pages 973--983

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    This publication is cited in the following articles:
    1. I. V. Konopleva, B. V. Loginov, “Gruppovaya simmetriya dinamicheskikh bifurkatsionnykh zadach so spektrom Shmidta v linearizatsii”, Vestn. NGU. Ser. matem., mekh., inform., 14:4 (2014), 50–63  mathnet
    2. D. V. Valovik, Yu. G. Smirnov, “Recent advances in the theory of coupled nonlinear guided waves”, 2014 xxxith ursi general assembly and scientific symposium (ursi gass), IEEE, 2014  isi
    3. E. Smolkin, Yu. Shestopalov, “Numerical study of multilayered nonlinear inhomogeneous waveguides in the case of te polarization”, 2016 10th european conference on antennas and propagation (eucap), Proceedings of the European Conference on Antennas and Propagation, IEEE, 2016  isi
    4. E. Smolkin, “The azimuthal symmetric hybrid waves in nonlinear cylindrical waveguide”, 2017 Progress in Electromagnetics Research Symposium–Spring, PIERS, IEEE, 2017, 348–353  crossref  isi
    5. D. V. Semenikhina, N. N. Gorbatenko, “Analysis of excitation of nonlinear loaded perfectly conducting cylinder coated with the layer of metamaterial using method of integral equations”, 2017 Radiation and Scattering of Electromagnetic Waves, RSEMW, IEEE, 2017, 197–200  crossref  isi
    6. 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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