S.A. Kapustin – Post-graduate Student,

Nizhny Novgorod State Technical University n.a. R.E. Alekseev

A.V. Lvutin – Post-graduate Student,

Nizhny Novgorod State Technical University n.a. R.E. Alekseev

Yu.V. Raevskaya – Ph.D. (Eng.), Associate Professor,  

Nizhny Novgorod State Technical University n.a. R.E. Alekseev

А.А. Titarenko – Dr.Sc. (Eng.), Professor,  

Nizhny Novgorod State Technical University n.a. R.E. Alekseev

E-mail: physics@nntu.nnov.ru; Kapustin_1994@mail.ru

The fundamental feature of the solutions of non-self-adjoint boundary-value electrodynamic problems is (in contrast to self-adjoint ones) the frequency dependence of their spatial distributions. In this regard, in particular, the classification of waves described by solutions of non-self-adjoint boundary value problems according to the structures of their fields (as is done in the case of waves described by self-adjoint operators) turns out to be illegal.

In non-self-adjoint boundary value problems, in the general case, there is no continuity of the branches of solutions corresponding to propagating and transcendental waves. The dispersion characteristics of these waves are connected by branches of solutions of the dispersion equations corresponding to complex waves. The coordination of the branches of solutions of the dispersion equations takes place with the correct choice of the complex plane of their search. For open guiding structures described by non-self-adjoint operators, degeneration and quasi-degeneration of wave spectra, their transformation and interaction are characteristic.

The aim of this work is to identify the features of dispersion problems (problems of studying wave spectra) for guiding structures described by non-self-adjoint boundary value problems, and to compare them with dispersion problems of self-adjoint operators. The article discusses the features of dispersion problems for waves in guiding structures described by non-self-adjoint operators. In order to obtain a priori information about the wave spectra of the guiding structures, it is proposed to make a transition from the boundary value problem to an integral equation with a strict asymptotic representation of the solution.

The article presents a general scheme for solving non-self-adjoint boundary-value electrodynamic problems.

To determine the wave spectrum of electrodynamic structures, first of all, it is necessary to determine the type of operator, investigate the possibility of reducing the boundary value problem to an integral equation, find out the possibility of obtaining its asymptotic solutions, analyze the functions that form the characteristic (dispersion) equation for the nature of its complexity, from the nature of the complexity of the dispersion equations find out the possibility of forming a self-consistent boundary value problem.

Kapustin S.A., Lvutin A.V., Raevskaya Yu.V., Titarenko A.A. Non-self-connected boundary-value problems for inhomogeneous guiding electrodynamic structures. Achievements of modern radioelectronics. 2020. V. 74. № 9. P. 37–43. DOI: 10.18127/j20700784-202009-04. [in Russian]

1. Naymark M.A. Lineynye differentsial'nye operatory. M.: Nauka. 1969. [in Russian]
2. Kamke E. Spravochnik po obyknovennym differentsial'nym uravneniyam. M.: Nauka. 1965. [in Russian]
3. Vaynshteyn L.A. Elektromagnitnye volny. M.: Radio i svyaz'. 1988. [in Russian]
4. Neganov V.A., Osipov O.V., Raevskiy S.B., Yarovoy G.P. Elektrodinamika i rasprostranenie radiovoln. M.: Radiotekhnika. 2009. [in Russian]
5. Tikhonov A.N., Samarskiy A.A. Uravneniya matematicheskoy fiziki. M.: Nauka. 1977. [in Russian]
6. Madelung E. Matematicheskiy apparat fiziki. M.: Gos. izd-vo fiz.-mat. lit-ry. 1961. [in Russian]
7. Al'khovskiy E.A., Il'inskiy A.S., Troshin G.I. Issledovanie gofrirovannykh volnovodov. Radiotekhnika i elektronika. 1974. T. 19. № 6. S. 1136–1141. [in Russian]
8. Veselov G.I., Raevskiy S.B. Sloistye metallo-dielektricheskie volnovody. M.: Radio i svyaz'. 1988. [in Russian]
9. Raevskiy A.S., Raevskiy S.B. Neodnorodnye napravlyayushchie struktury, opisyvaemye nesamosopryazhennymi operatorami. M.:  Radiotekhnika. 2004. [in Russian]
10. Raevskiy A.S., Raevskiy S.B. Kompleksnye volny. M.: Radiotekhnika. 2010. [in Russian]
11. Belyantsev A.I., Gaponov A.V. O volnakh s kompleksnymi postoyannymi rasprostraneniya v svyazannykh liniyakh peredachi bez dissipatsii energii. Radiotekhnika i elektronika. 1964. T. 9. № 7. S. 1118–1195. [in Russian]
12. Kogtev A.S., Raevskiy S.B. O kompleksnykh volnakh v sloistykh ekranirovannykh volnovodakh. Radiotekhnika i elektronika, 1991. T. 36. S. 652–658. [in Russian]
13. Shevchenko V.V. Vyrozhdenie i kvazivyrozhdenie spektra i preobrazovanie voln v dielektricheskikh volnovodakh i svetovodakh. Radiotekhnika i elektronika. 2000. T. 45. № 10. S. 1157–1167. [in Russian]