Physics of Wave Processes and Radio SystemsPhysics of Wave Processes and Radio Systems1810-31892782-294XPovolzhskiy State University of Telecommunications and Informatics748910.18469/1810-3189.2019.22.3.5-9UnknownDetermination of the spectra of solutions of boundary value problems for guiding structures using the transition to integral equationsKapustinS.A.physics@nntu.ruNovoselovaN.A.physics@nntu.nnov.ruRaevskiiA.S.physics@nntu.ruRaevskiiS.B.raevsky@nntu.ruNizhny Novgorod State Technical University named after R.E. Alekseev010320192235907122019Copyright © 2019, Kapustin S., Novoselova N., Raevskii A., Raevskii S.2019<p>The vast majority of guiding structures are described [13] by non-self-adjoint electrodynamic operators, which are understood as the totality of the differential equation and the system of boundary conditions. In [15], 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 [56] 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.</p>electrodynamic operatorwave spectrumboundary value problemVolterra equationeigen and improper wavestwo-layer guiding structuresэлектродинамический операторспектр волнкраевая задачауравнение Вольтеррасобственные и несобственные волныдвухслойные направляющие структуры[<ol><li>Veselov G.I., Raevskij S.B. Sloistye metallo-dielektricheskie volnovody [Layered metal-dielectric waveguides]. M.: Radio i svjaz’, 1988, 248 p. [in Russian].</li><li>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].</li><li>Raevskij A.S., Raevskij S.B. Kompleksnye volny [Complex waves]. M.: Radiotehnika, 2010, 223 p. [in Russian].</li><li>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].</li><li>Najmark M.A. Linejnye differentsial’nye operatory [Linear differential operators]. M.: Nauka, 1969, 528 p. [in Russian].</li><li>Kamke E. Spravochnik po obyknovennym differentsial’nym uravnenijam [Handbook of ordinary differential equations]. M.: Nauka, 1965, 703 p. [in Russian].</li><li>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].</li><li>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].</li><li>Zabrejko P.P. [et al.] Integral’nye uravnenija [Integral Equations]. M.: Nauka, 1968, 448 p. [in Russian].</li><li>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].</li><li>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].</li><li>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].</li></ol>]