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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2021, Volume 61, Number 1, Pages 108–123
DOI: https://doi.org/10.31857/S0044466921010099 (Mi zvmmf11187) 		 
This article is cited in 9 scientific papers (total in 9 papers)

Mathematical physics

Perturbation method in the theory of propagation of two-frequency electromagnetic waves in a nonlinear waveguide I: TE-TE waves

D. V. Valovik

Penza State University
Full-text PDF Citations (9)
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DOI: https://doi.org/10.31857/S0044466921010099
Abstract: The article deals with the problem of propagation of a two-frequency electromagnetic wave in a waveguide filled with a nonlinear medium. A two-frequency wave is the sum of two monochromatic TE waves with different frequencies. The permittivity of the waveguide is characterized by a very general nonlinearity function corresponding to self-action effects. It is shown that, under certain conditions, the two-frequency wave is an eigenmode of the waveguide. From a mathematical point of view, the problem reduces to a nonlinear two-parameter eigenvalue problem for the system of (nonlinear) Maxwell’s equations. The main result of the article is the proof of the existence of nonlinearizable solutions of the problem.
Key words: Maxwell's equations, nonlinear permittivity, planar dielectric waveguide, nonlinear Sturm–Liouville-type problem, two-parameter eigenvalue problem, perturbation method, integral characteristic equation.
Funding agency Grant number
Russian Science Foundation 18-71-10015
This work was supported by the Russian Science Foundation (project no. 18-71-10015).
Received: 06.02.2020
Revised: 06.02.2020
Accepted: 18.09.2020
English version:
Computational Mathematics and Mathematical Physics, 2021, Volume 61, Issue 1, Pages 103–117
DOI: https://doi.org/10.1134/S0965542521010097
Bibliographic databases:
Document Type: Article
UDC: 517.958
Language: Russian
Citation: D. V. Valovik, “Perturbation method in the theory of propagation of two-frequency electromagnetic waves in a nonlinear waveguide I: TE-TE waves”, Zh. Vychisl. Mat. Mat. Fiz., 61:1 (2021), 108–123; Comput. Math. Math. Phys., 61:1 (2021), 103–117
Citation in format AMSBIB
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    • This publication is cited in the following 9 articles:
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