Geodesic
Eigenvalue transmission problems describing the propagation of TE and TM waves in two-layered inhomogeneous anisotropic cylindrical and planar waveguides
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 3, pp. 460-468 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Problems on the propagation of surface TE and TM waves in an inhomogeneous anisotropic two-layered planar or cylindrical magneto-dielectric waveguide are considered. The problem is reduced to the analysis of a Sturm–Liouville problem of a special kind with boundary conditions of the third kind, nonlinearly depending on the spectral parameter. The conditions under which TE and TM waves can propagate are obtained, and the regions of localization of the corresponding propagation constants are determined. 
@article{ZVMMF_2015_55_3_a9,
     author = {Yu. G. Smirnov},
     title = {Eigenvalue transmission problems describing the propagation of {TE} and {TM} waves in two-layered inhomogeneous anisotropic cylindrical and planar waveguides},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {460--468},
     year = {2015},
     volume = {55},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_3_a9/}
}
TY  - JOUR
AU  - Yu. G. Smirnov
TI  - Eigenvalue transmission problems describing the propagation of TE and TM waves in two-layered inhomogeneous anisotropic cylindrical and planar waveguides
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2015
SP  - 460
EP  - 468
VL  - 55
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_3_a9/
LA  - ru
ID  - ZVMMF_2015_55_3_a9
ER  - 
%0 Journal Article
%A Yu. G. Smirnov
%T Eigenvalue transmission problems describing the propagation of TE and TM waves in two-layered inhomogeneous anisotropic cylindrical and planar waveguides
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2015
%P 460-468
%V 55
%N 3
%U http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_3_a9/
%G ru
%F ZVMMF_2015_55_3_a9
Yu. G. Smirnov. Eigenvalue transmission problems describing the propagation of TE and TM waves in two-layered inhomogeneous anisotropic cylindrical and planar waveguides. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 3, pp. 460-468. http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_3_a9/

[1] Vainshtein L. A., Elektromagnitnye volny, Radio i svyaz, M., 1988

[2] Samarskii A. A., Tikhonov A. N., “O vozbuzhdenii radiovolnovodov, I”, Zhurnal teoret. fiz., 17:11 (1947), 1283–1296

[3] Samarskii A. A., Tikhonov A. N., “O vozbuzhdenii radiovolnovodov, II”, Zhurnal teoret. fiz., 17:12 (1947), 1431–1440

[4] Samarskii A. A., Tikhonov A. N., “O predstavlenii polya v volnovode v vide summy polei TE i TM”, Zhurnal teoret. fiz., 18:7 (1948), 971–985

[5] Krasnushkin P. E., Moiseev E. I., “O vozbuzhdenii vynuzhdennykh kolebanii v sloistom radiovolnovode”, Dokl. AN SSSR, 264:5 (1982), 1123–1127 | MR

[6] Smirnov Yu. G., “O polnote sistemy sobstvennykh i prisoedinennykh voln chastichno zapolnennogo volnovoda s neregulyarnoi granitsei”, Dokl. AN SSSR, 297:4 (1987), 829–832

[7] Smirnov Yu. G., “Primenenie metoda operatornykh puchkov v zadache o sobstvennykh volnakh chastichno zapolnennogo volnovoda”, Dokl. AN SSSR, 312:3 (1990), 597–599

[8] Smirnov Yu. G., “Metod operatornykh puchkov v kraevykh zadachakh sopryazheniya dlya sistemy ellipticheskikh uravnenii”, Differents. ur-niya, 27:1 (1991), 140–147 | MR | Zbl

[9] Delitsyn A. L., “O postanovke kraevykh zadach dlya sistemy uravnenii Maksvella v tsilindre i ikh razreshimosti”, Izv. RAN. Ser. matem., 71:3 (2007), 60–111

[10] Smirnov Yu. G., Matematicheskie metody issledovaniya zadach elektrodinamiki, Informatsionno-izdatelskii tsentr PGU, Penza, 2009

[11] Shestopalov Yu., Smirnov Yu., “Eigenwaves in waveguides with dielectric inclusions: spectrum”, Applicable Analysis: An International Journal, 2013, 778980–779000

[12] Shestopalov Yu., Smirnov Yu., “Eigenwaves in waveguides with dielectric inclusions: completeness”, Applicable Analysis: An International Journal, 2013, 850494–850514

[13] Dautov R. Z., Karchevskii E. M., Metod integralnykh uravnenii i tochnye nelokalnye granichnye usloviya v teorii dielektricheskikh volnovodov, Izd-vo Kazanskogo gos. un-ta, Kazan, 2009

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

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

[16] Kurant R., Gilbert D., Metody matematicheskoi fiziki, v. 1, Gostekhizdat, M.–L., 1951