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Zh. Vychisl. Mat. Mat. Fiz., 2019, Volume 59, Number 5, Pages 838–858 (Mi zvmmf10896)  

This article is cited in 1 scientific paper (total in 1 paper)

Propagation of electromagnetic waves in an open planar dielectric waveguide filled with an nonlinear medium I: TE waves

D. V. Valovik

Penza State University, Penza, 440026 Russia

Abstract: A nonlinear Sturm–Liouville-type eigenvalue problem on an interval with the boundary conditions of the third kind and an additional (local) condition at one of the ends of the interval is studied. The nonlinearity in the equation is specified by a nonnegative monotonically increasing function, and the boundary conditions depend nonlinearly on the spectral parameter. Such a problem describes the propagation of monochromatic electromagnetic TE waves in a planar dielectric waveguide filled with a nonlinear medium. The nonlinearity function covers a wide range of laws of nonlinear optics corresponding to the self-action effects. Results on the solvability of the problem and the properties of eigenvalues are obtained.

Key words: Maxwell's equations, nonlinear eigenvalue problem, nonlinear Sturm–Liouville problem, asymptotics of eigenvalues, comparison theorem, 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.


DOI: https://doi.org/10.1134/S0044466919060139


English version:
Computational Mathematics and Mathematical Physics, 2019, 59:6, 958–977

Bibliographic databases:

UDC: 519.634
Received: 12.09.2018
Revised: 19.01.2019
Accepted:08.02.2019

Citation: D. V. Valovik, “Propagation of electromagnetic waves in an open planar dielectric waveguide filled with an nonlinear medium I: TE waves”, Zh. Vychisl. Mat. Mat. Fiz., 59:5 (2019), 838–858; Comput. Math. Math. Phys., 59:6 (2019), 958–977

Citation in format AMSBIB
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\jour Zh. Vychisl. Mat. Mat. Fiz.
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\pages 838--858
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\jour Comput. Math. Math. Phys.
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\pages 958--977
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. D. V. Valovik, “On the integral characteristic function of the Sturm-Liouville problem”, Sb. Math., 211:11 (2020), 1539–1550  mathnet  crossref  crossref  mathscinet  isi  elib
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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