Enviar artigo por via de e-mail ON THE NON-INERT PERTURBATION METHOD FOR PROVING THE EXISTENCE OF NON-LINEARIZABLE SOLUTIONS IN A NONLINEAR EIGENVALUE PROBLEM ARISING IN THE THEORY OF WAVEGUIDES
- Autores: Valovik D.V1, Dyundyaeva A.A2, Tikhov S.V1
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Afiliações:
- Penza State University
- Edição: Volume 64, Nº 10 (2024)
- Páginas: 1949-1965
- Seção: Mathematical physics
- URL: https://bakhtiniada.ru/0044-4669/article/view/277063
- DOI: https://doi.org/10.31857/S0044466924100135
- EDN: https://elibrary.ru/JYXPYU
- ID: 277063
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Resumo
The problem of propagation of electromagnetic waves in a plane dielectric waveguide is studied. The waveguide is filled with a nonlinear inhomogeneous medium; the nonlinearity is characterized by an arbitrary monotone positive continuously differentiable function with a stepwise increase on infinity. The inhomogeneity of the medium is characterized by small (non-monotone) perturbations of the linear part of the dielectric permeability, as well as the coefficient at the nonlinear term. From a mathematical point of view, this problem is equivalent to the eigenvalue problem for a system of Maxwell equations with mixed boundary conditions. To study the problem, a perturbation method is proposed, in which a simpler nonlinear problem is used as the main problem. The existence of both linearizable and non-linearizable solutions is proved.
Sobre autores
D. Valovik
Penza State University
Email: dvalovik@mail.ru
Penza
A. Dyundyaeva
S. Tikhov
Penza State University
Email: tik.stanislav2015@yandex.ru
Penza
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