Geodesic
Multiplicity of eigenvalues in certain boundary value problems for the Helmholtz equation
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 53 (2013) no. 5, pp. 783-791 
V. A. Malakhov; A. V. Nazarov; A. S. Raevskii; S. B. Raevskii. Multiplicity of eigenvalues in certain boundary value problems for the Helmholtz equation. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 53 (2013) no. 5, pp. 783-791. http://geodesic.mathdoc.fr/item/ZVMMF_2013_53_5_a8/
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     title = {Multiplicity of eigenvalues in certain boundary value problems for the {Helmholtz} equation},
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Voir la notice de l'article provenant de la source Math-Net.Ru

Boundary value problems for two-layer cylindrical waveguides (namely, for a circular two-layer closed waveguide and a dielectric waveguide in an unbounded medium) are considered. It is shown that the same eigenvalues determining the wave numbers of waves in the waveguides can correspond to different solutions of the boundary value problem.

[1] Veselov G. I., Raevskii S. B., “Kompleksnye volny v poperechno-neodnorodnykh napravlyayuschikh strukturakh”, Radiotekhn., 42:8 (1987), 64–67

[2] Veselov G. I., Raevskii S. B., Sloistye metallo-dielektricheskie volnovody, Radio i svyaz, M., 1988, 248 pp.

[3] Raevskii A. S., Raevskii S. B., Titarenko A. A., “Osnovnaya osobennost napravlyayuschikh struktur, opisyvaemykh nesamosopryazhennymi operatorami”, Pisma v ZhTF, 30:1 (2004), 56–64 | MR

[4] Raevskii A. S., Raevskii S. B., Neodnorodnye napravlyayuschie struktury, opisyvaemye nesamosopryazhennymi operatorami, Radiotekhn., M., 2004

[5] Vipritskii D. D., Nazarov A. V., Raevskii S. B., “O kompleksnykh volnakh v nevzaimnykh napravlyayuschikh strukturakh”, Pisma v ZhTF, 33:5 (2007), 1–11

[6] Raevskii A. S., Raevskii S. B., Kompleksnye volny, Radiotekhn., M., 2010

[7] Naimark M. A., Lineinye differentsialnye operatory, Nauka, M., 1969 | MR

[8] Raevskii S. B., “Kompleksnye volny v dvukhsloinom kruglom ekranirovannom volnovode”, Izv. Vuzov SSSR. Radiofiz., 15:1 (1972), 112–116

[9] Raevskii S. B., “O suschestvovanii kompleksnykh voln v nekotorykh dvukhsloinykh izotropnykh strukturakh”, Izv. Vuzov SSSR. Radiofiz., 15:12 (1972), 1926–1931

[10] Shevchenko V. V., “Naglyadnaya klassifikatsiya voln, napravlyaemykh regulyarnymi otkrytymi volnovodami”, Radiotekhn. i elektronika, 12:10 (1969), 1768–1772 | MR

[11] Malakhov V. A., Raevskii A. S., Raevskii S. B., “Prisoedinennye volny v sloistykh napravlyayuschikh strukturakh”, Antenny, 2010, no. 12, 44–50

[12] Malakhov V. A., Raevskii A. S., Raevskii S. B., “Prisoedinennye volny v kruglom dvukhsloinom ekranirovannom volnovode”, Pisma v ZhTF, 2011, no. 2, 71–79

[13] Krasnushkin P. E., Fedorov E. N., “O kratnosti volnovykh chisel normalnykh voln v sloistykh sredakh”, Radiotekhn. i elektronika, 17:6 (1972), 1129–1140 | MR

[14] Ilinskii A. S., Slepyan G. Ya., Kolebaniya i volny v elektrodinamicheskikh sistemakh s poteryami, Izd-vo MGU, M., 1983 | MR

[15] Raevskii S. B., “Prisoedinennye volny v sloistykh tsilindricheskikh napravlyayuschikh strukturakh”, Vestn. VVO ATN RF. Ser. Vysokie tekhnologii v radioelektron., 1995, no. 1, 57–60

[16] Malakhov V. A., Raevskii A. S., Raevskii S. B., “Added Solutions of Boundary Value Problems for Double-Layer Guiding Structures”, Intern. J. Electromagnetics and Applications, 2:5 (2012), 114–119 | DOI