Email this article Determination of the spectra of solutions of boundary value problems for guiding structures using the transition to integral equations
- Authors: Kapustin S.1, Novoselova N.1, Raevskii A.1, Raevskii S.1
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Affiliations:
- Nizhny Novgorod State Technical University named after R.E. Alekseev
- Issue: Vol 22, No 3 (2019)
- Pages: 5-9
- Section: Articles
- URL: https://journals.ssau.ru/pwp/article/view/7489
- DOI: https://doi.org/10.18469/1810-3189.2019.22.3.5-9
- ID: 7489
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Abstract
The vast majority of guiding structures are described [1–3] by non-self-adjoint electrodynamic operators, which are understood as the totality of the differential equation and the system of boundary conditions. In [1–5], the conditions for the non-self-adjointness of electrodynamic operators are formulated as applied to the method of separation of variables. The indicated operators can be put in accordance with [5–6] integral equations. The boundary problems for cylindrical guiding structures are assigned the Volterra integral equations, using asymptotic solutions of which an a priori determination of the spectra of solutions of boundary-value problems for two-layer open and shielded waveguides is carried out.
About the authors
S.A. Kapustin
Nizhny Novgorod State Technical University named after R.E. Alekseev
Author for correspondence.
Email: physics@nntu.ru
N.A. Novoselova
Nizhny Novgorod State Technical University named after R.E. Alekseev
Email: physics@nntu.nnov.ru
A.S. Raevskii
Nizhny Novgorod State Technical University named after R.E. Alekseev
Email: physics@nntu.ru
S.B. Raevskii
Nizhny Novgorod State Technical University named after R.E. Alekseev
Email: raevsky@nntu.ru
References
- Veselov G.I., Raevskij S.B. Sloistye metallo-dielektricheskie volnovody [Layered metal-dielectric waveguides]. M.: Radio i svjaz’, 1988, 248 p. [in Russian].Raevskij A.S. Elektrodinamika napravljajuschih i rezonansnyh struktur, opisyvaemyh nesamosoprjazhennymi kraevymi zadachami [Electrodynamics of the guiding and resonant structures described nonselfadjoint edge], 2004, 450 p. [in Russian].Raevskij A.S., Raevskij S.B. Kompleksnye volny [Complex waves]. M.: Radiotehnika, 2010, 223 p. [in Russian].Raevskij A.S., Raevskij S.B. Neodnorodnye napravljajuschie struktury, opisyvaemye nesamosoprjazhennymi operatorami [Heterogeneous guiding structures described nonselfadjoint operators]. M.: Radiotehnika, 2004, 110 p. [in Russian].Najmark M.A. Linejnye differentsial’nye operatory [Linear differential operators]. M.: Nauka, 1969, 528 p. [in Russian].Kamke E. Spravochnik po obyknovennym differentsial’nym uravnenijam [Handbook of ordinary differential equations]. M.: Nauka, 1965, 703 p. [in Russian].Shevchenko V.V. Nagljadnaja klassifikatsija voln, napravljaemyh reguljarnymi otkrytymi volnovodami [Transparent classification of waves guided by regular open waveguides]. Radiotehnika i elektronika [Technology and Electronics], 1969, vol. 12, no. 12, pp. 1768–1773 [in Russian].Raevskij A.S., Raevskij S.B. Kraevaja zadacha na prisoedinennom uravnenii Gel’mgol’tsa [Boundary value problem on the attached Helmholtz equation]. Radiotehnika i elektronika [Technology and Electronics], 2016, vol. 61, no. 3, pp. 233–244 [in Russian].Zabrejko P.P. [et al.] Integral’nye uravnenija [Integral Equations]. M.: Nauka, 1968, 448 p. [in Russian].Shevchenko V.V. O razlozhenii polej otkrytyh volnovodov po sobstvennym i nesobstvennym volnam [On the expansion of the fields of open waveguides of proper and improper waves]. Radiotehnika i elektronika [Technology and Electronics], 1971, vol. 14, no. 8, pp. 1242–1249 [in Russian].Shevchenko V.V. Poverhnostnye i vytekajuschie volny ploskogo dielektricheskogo volnovoda s poterjami [Surface and leaky waves planar dielectric waveguide losses]. Radiotehnika i elektronika [Technology and Electronics], 1988, vol. 31, no. 3, pp. 456–465 [in Russian].Raevskij A.S. Issledovanie spektrov voln neodnorodnyh otkrytyh napravljajuschih struktur [Spectra waves heterogeneous open guiding structures]. Fizika volnovyh protsessov i radiotehnicheskie sistemy [Physics of wave processes and radio systems], 2006, vol. 9, no. 3, pp. 66–70 [in Russian].
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