Geodesic
Numerical investigation of trapped modes in an irregular waveguide
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 46 (2006) no. 3, pp. 501-508 
A. V. Tikhonov. Numerical investigation of trapped modes in an irregular waveguide. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 46 (2006) no. 3, pp. 501-508. http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_3_a13/
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Voir la notice de l'article provenant de la source Math-Net.Ru

It is shown by means of a numerical experiment that an arbitrary asymmetric perturbation of the function describing a dielectric insert in a waveguide, in the general case, results in vanishing of the trapped mode; i.e., it ceases to exist.

[1] Reilich F., “Das Eigenwertproblem von $\Delta u+\lambda u=0$ in Halbrohren”, Studies and Essays Presented to R. Courant on his 60th Birthday, Intersci. Publs, Inc., New York, 1948, 329–344 | MR

[2] Jones D. S., “The eigenvalues of $\nabla^2 u+\lambda u=0$ when the boundary conditions are on semi-infinite domains”, Proc. Cambridge Soc., 49 (1951), 668–684 | DOI | MR

[3] Sveshnikov A. G., “Printsip predelnogo pogloscheniya dlya volnovodov”, Dokl. AN SSSR, 80:3 (1951), 345–347 | Zbl

[4] Ilinskii A. C., Kravtsov V. V., Sveshnikov A. G., Matematicheskie modeli elektrodinamiki, Vyssh. shkola, M., 1991

[5] Delitsyn A. L., “O zadache rasseyaniya na neodnorodnosti v volnovode”, Zh. vychisl. matem. i matem. fiz., 40:4 (2000), 606–610 | MR | Zbl

[6] Norri D., Friz Zh., Vvedenie v metod konechnykh elementov, Mir, M., 1981 | MR | Zbl

[7] Flannery B. P., Press W. H., Teukolsky S. A., Veiterling W. T., Numerical recipes, Cambridge Univ. Press, New York, 1992

[8] Bogolyubov A. H., Delitsyn A. L., Malykh M. D., “O lovushechnykh modakh volnoveduschikh sistem”, Vestn. MGU, 2001, no. 6, 65–66 | Zbl