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Zh. Vychisl. Mat. Mat. Fiz., 2019, Volume 59, Number 5, Pages 762–774 (Mi zvmmf10890)  

On a nonlinear spectral problem for a dielectric waveguide with Kerr nonlinearity

A. L. Delitsynab, L. L. Delitsyncde

a National Research University Higher School of Economics, Moscow, 125319 Russia
b Institute for Information Transmission Problems, Russian Academy of Sciences, Moscow, 127051 Russia
c Lomonosov Moscow State University, Moscow, 125009 Russia
d Main Scientific Research Test Center of Robotics, Ministry of Defense of the Russian Federation, Moscow, 119001 Russia
e Moscow State Institute of Culture, Khimki, Moscow oblast, 125319 Russia

Abstract: The frequency dependence of the propagation constants of plane layered dielectric waveguides with the Kerr nonlinearity is considered. An explanation to the possible difference of their behavior from the linear case, related exclusively to a fixed value of an eigenfunction at the boundary of the layer, is given. Explicit formulas for calculating the dispersion curves are obtained. Their behavior for different ways of defining the eigenfunction of the nonlinear problem is analyzed.

Key words: nonlinear eigenvalue problem, Kerr nonlinearity, planar waveguides.

Funding Agency Grant Number
Russian Science Foundation 14-50-00150
A.L. Delitsyn's work was supported by the Russian Science Foundation at the Institute for Information Transmission Problems of the Russian Academy of Sciences (project no. 14-50-00150).


DOI: https://doi.org/10.1134/S0044466919050065


English version:
Computational Mathematics and Mathematical Physics, 2019, 59:5, 718–730

Bibliographic databases:

UDC: 519.634
Received: 29.08.2018
Revised: 29.08.2018
Accepted:11.01.2019

Citation: A. L. Delitsyn, L. L. Delitsyn, “On a nonlinear spectral problem for a dielectric waveguide with Kerr nonlinearity”, Zh. Vychisl. Mat. Mat. Fiz., 59:5 (2019), 762–774; Comput. Math. Math. Phys., 59:5 (2019), 718–730

Citation in format AMSBIB
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\jour Zh. Vychisl. Mat. Mat. Fiz.
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\issue 5
\pages 762--774
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