Geodesic
The asymptotic eigenfunctions of the operator $\nabla D(x,y)\nabla$ corresponding to Liouville metrics and waves on water captured by bottom irregularities
Matematičeskie zametki, Tome 64 (1998) no. 3, pp. 414-422 
V. S. Matveev. The asymptotic eigenfunctions of the operator $\nabla D(x,y)\nabla$ corresponding to Liouville metrics and waves on water captured by bottom irregularities. Matematičeskie zametki, Tome 64 (1998) no. 3, pp. 414-422. http://geodesic.mathdoc.fr/item/MZM_1998_64_3_a9/
@article{MZM_1998_64_3_a9,
     author = {V. S. Matveev},
     title = {The asymptotic eigenfunctions of the operator $\nabla D(x,y)\nabla$ corresponding to {Liouville} metrics and waves on water captured by bottom irregularities},
     journal = {Matemati\v{c}eskie zametki},
     pages = {414--422},
     year = {1998},
     volume = {64},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1998_64_3_a9/}
}
TY  - JOUR
AU  - V. S. Matveev
TI  - The asymptotic eigenfunctions of the operator $\nabla D(x,y)\nabla$ corresponding to Liouville metrics and waves on water captured by bottom irregularities
JO  - Matematičeskie zametki
PY  - 1998
SP  - 414
EP  - 422
VL  - 64
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/MZM_1998_64_3_a9/
LA  - ru
ID  - MZM_1998_64_3_a9
ER  - 
%0 Journal Article
%A V. S. Matveev
%T The asymptotic eigenfunctions of the operator $\nabla D(x,y)\nabla$ corresponding to Liouville metrics and waves on water captured by bottom irregularities
%J Matematičeskie zametki
%D 1998
%P 414-422
%V 64
%N 3
%U http://geodesic.mathdoc.fr/item/MZM_1998_64_3_a9/
%G ru
%F MZM_1998_64_3_a9

Voir la notice de l'article provenant de la source Math-Net.Ru

We construct a set of examples of bottom reliefs for which there exist captured waves corresponding to quasimodes of the wave operator $\nabla D(x,y)\nabla$.

[1] Dobrokhotov S. Yu., “Asimptotiki poverkhnostnykh voln, zakhvachennykh beregami i neodnorodnostyami relefa dna”, Dokl. AN SSSR, 289:3 (1986), 575–579 | MR

[2] Le Blon P., Maisek L., Volny v okeane, T. 1, Mir, M., 1981

[3] Maslov V. P., Fedoryuk M. B., Kvaziklassicheskoe priblizhenie dlya uravnenii kvantovoi mekhaniki, Nauka, M., 1976

[4] Dobrokhotov S. Yu., Zhevandrov P. N., Asimptoticheskie razlozheniya i kanonicheskii operator Maslova v lineinoi teorii poverkhnostnykh gravitatsionnykh voln: osnovnye uravneniya i konstruktsii, Preprint IPM AN SSSR No. 328, IPM, M., 1988

[5] Dobrokhotov S. Yu., Zhevandrov P. N., “Nestandartnye kharakteristiki i operatornyi metod Maslova v lineinykh zadachakh o neustanovivshikhsya volnakh na vode”, Funktsion. analiz i ego prilozh., 19:4 (1985), 43–54 | MR | Zbl

[6] Kosygin D. V., Minasov A. A., Sinai Ya. G., “Statisticheskie svoistva spektrov operatorov Laplasa–Beltrami na poverkhnostyakh Liuvillya”, UMN, 48:4 (292) (1993), 3–130 | MR | Zbl

[7] Arnold V. I., Matematicheskie metody klassicheskoi mekhaniki, Nauka, M., 1979 | Zbl

[8] Selivanova E. N., “Traektornye izomorfizmy liuvillevykh sistem na dvumernom tore”, Matem. sb., 186:10 (1995), 141–160 | MR | Zbl

[9] Kolokoltsev V. N., Polinomialnye integraly geodezicheskikh potokov na kompaktnykh poverkhnostyakh, Diss. ... k. f.-m. n., MIEM, M., 1984