Geodesic
Combined method of calculation of the field of the point source in a wave guide
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 32, Tome 297 (2003), pp. 116-135 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

The two-dimensional problem of propagation of waves, raised by a point source, in an interior wave guide is investigated. The Dirichlet (Neumann) boundary condition is given on the upper (lower) bound of the wave guide. The possibility of representation of the exact solution as a sum of the geometro-optical waves, the normal waves and the residual is shown. The sufficient conditions on the general amount of the detached normal and geometro-optical waves are obtained. The residual is expressed by the simple formula. 
@article{ZNSL_2003_297_a7,
     author = {N. Ya. Kirpichnikova and V. B. Philippov and N. G. Vlasjuk},
     title = {Combined method of calculation of the field of the point source in a~wave guide},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {116--135},
     year = {2003},
     volume = {297},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2003_297_a7/}
}
TY  - JOUR
AU  - N. Ya. Kirpichnikova
AU  - V. B. Philippov
AU  - N. G. Vlasjuk
TI  - Combined method of calculation of the field of the point source in a wave guide
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2003
SP  - 116
EP  - 135
VL  - 297
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2003_297_a7/
LA  - ru
ID  - ZNSL_2003_297_a7
ER  - 
%0 Journal Article
%A N. Ya. Kirpichnikova
%A V. B. Philippov
%A N. G. Vlasjuk
%T Combined method of calculation of the field of the point source in a wave guide
%J Zapiski Nauchnykh Seminarov POMI
%D 2003
%P 116-135
%V 297
%U http://geodesic.mathdoc.fr/item/ZNSL_2003_297_a7/
%G ru
%F ZNSL_2003_297_a7
N. Ya. Kirpichnikova; V. B. Philippov; N. G. Vlasjuk. Combined method of calculation of the field of the point source in a wave guide. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 32, Tome 297 (2003), pp. 116-135. http://geodesic.mathdoc.fr/item/ZNSL_2003_297_a7/

[1] V. M. Babich, V. S. Buldyrev, V. B. Filippov, “Korotkovolnovaya asimptotika v zadache difraktsii na vognutoi poverkhnosti”, XI Vsesoyuznyi simpozium po rasprostraneniyu radiovoln, 3, Nauka, M., 1975, 47–50

[2] V. B. Filippov, “Korotkovolnovaya asimptotika toka i diagramma napravlennosti dlya zadachi difraktsii na neploskikh ekranakh”, VII Vsesoyuznyi simpozium po difraktsii i rasprostraneniya voln, 1, Nauka, Rostov n/D, 1977, 47–50

[3] V. B. Philippov, “Diffraction by a nonplanar screen”, Wave Motion, 3 (1981), 78–81 | DOI

[4] V. B. Filippov, “Ob odnom metode rascheta polya tochechnogo istochnika v volnovode”, Zap. nauchn. semin. LOMI, 99, 1980, 146–156 | Zbl

[5] N. Ya. Kirpichnikova, V. B. Filippov, N. G. Vlasyuk, “Kombinirovannyi metod rascheta polya tochechnogo istochnika v vodnovode”, Zap. nauchn. semin. POMI, 257, 1999, 56–74 | MR | Zbl

[6] V. S. Buldyrev, “Pole tochechnogo istochnika v volnovode”, Trudy MIAN SSSR, CXV, 1971, 78–102 | MR | Zbl

[7] V. S. Buldyrev, “Asimptotika reshenii volnovogo uravneniya, sosredotochennykh vblizi osi ploskogo volnovoda v neodnorodnoi srede”, Problemy matematicheskoi fiziki. Vyp. 3, Izd-vo LGU, Leningrad, 1968, 5–30 | MR

[8] V. S. Buldyrev, A. I. Lanin, Z. A. Yanson, “Vychislenie polya na osi simmetrichnogo volnovoda”, Voprosy dinamicheskoi teorii rasprostraneniya seismicheskikh voln, 14 (1974), 84

[9] V. E. Grikurov, “Yavlenie perekrytiya prikausticheskikh zon v pripoverkhnostnom volnovode i svyazannoe s nim obobschenie luchevogo metoda”, Izv. VUZov, Radiofizika, 23:9 (1980), 1038 | MR

[10] A. S. Kryukovskii, D. S. Lukin, E. A. Palkin, “Chislennoe sravnenie dvukh asimptoticheskikh metodov reshenie zadach difraktsii voln v plavno neodnorodnykh sredakh”, Izv. VUZov, Radiofizika, 29:29 (1986), 9–88

[11] A. P. Kachalov, M. M. Popov, “Primenenie metoda summirovaniya gaussovykh puchkov dlya rascheta vysokochastotnykh volnovykh polei”, Dokl. AN SSSR, 258:5 (1981), 1097–1100

[12] A. P. Kachalov, M. M. Popov, Primenenie gaussovykh puchkov v izotropnoi teorii uprugosti, Preprint LOMI R-9-82, L., 1982

[13] A. S. Starkov, “Ob odnom metode rascheta polya tochechnogo istochnika v refraktsionnom volnovode”, Izv. VUZov, 32:11 (1989) | MR

[14] V. M. Kudryashov, “Geometrovolnovoi sposob vychisleniya akusticheskikh polei v volnovode”, Akusticheskii zhurnal, 22:5 (1976), 724–728

[15] A. Erdelyi, M. Wyman, “The asymptotic evaluation of certain integrals”, ARMA, 14:3 (1963), 217–260 | MR | Zbl

[16] L. B. Felsen, “Backscattering from wide-angle and narrow-angle cones”, J. Appl. Phys., 26:2 (1955), 138–151 | DOI | MR | Zbl

[17] L. B. Felsen, “Hybrid ray-mode fields in inhomogeneous waveguides and ducts”, J. Acoust. Soc. Amer., 69 (1981), 352–361 | DOI

[18] D. Ludwig, “Diffraction by a circular cavity”, J. Math. Phys., 11:5 (1970), 1617–1630 | DOI | MR

[19] L. M. Brekhovskikh, Akustika okeana, Nauka, M., 1974