Geodesic
Asymptotics for the solution of averaged equations for the system of coupled oscillators
Fundamentalʹnaâ i prikladnaâ matematika, Tome 12 (2006) no. 6, pp. 99-113 
L. A. Kalyakin; Yu. Yu. Bagderina. Asymptotics for the solution of averaged equations for the system of coupled oscillators. Fundamentalʹnaâ i prikladnaâ matematika, Tome 12 (2006) no. 6, pp. 99-113. http://geodesic.mathdoc.fr/item/FPM_2006_12_6_a6/
@article{FPM_2006_12_6_a6,
     author = {L. A. Kalyakin and Yu. Yu. Bagderina},
     title = {Asymptotics for the solution of averaged equations for the system of coupled oscillators},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {99--113},
     year = {2006},
     volume = {12},
     number = {6},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2006_12_6_a6/}
}
TY  - JOUR
AU  - L. A. Kalyakin
AU  - Yu. Yu. Bagderina
TI  - Asymptotics for the solution of averaged equations for the system of coupled oscillators
JO  - Fundamentalʹnaâ i prikladnaâ matematika
PY  - 2006
SP  - 99
EP  - 113
VL  - 12
IS  - 6
UR  - http://geodesic.mathdoc.fr/item/FPM_2006_12_6_a6/
LA  - ru
ID  - FPM_2006_12_6_a6
ER  - 
%0 Journal Article
%A L. A. Kalyakin
%A Yu. Yu. Bagderina
%T Asymptotics for the solution of averaged equations for the system of coupled oscillators
%J Fundamentalʹnaâ i prikladnaâ matematika
%D 2006
%P 99-113
%V 12
%N 6
%U http://geodesic.mathdoc.fr/item/FPM_2006_12_6_a6/
%G ru
%F FPM_2006_12_6_a6

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

The equations obtained by averaging the system of three weakly nonlinear oscillators are considered. Distinctive properties of asymptotics at infinity for the solutions of averaged equations for both constant and variable proper frequencies are studied.

[1] Arnold V. I., Dopolnitelnye glavy teorii obyknovennykh differentsialnykh uravnenii, Nauka, M, 1978 | MR

[2] Blombergen N., Nelineinaya optika, Mir, M, 1966

[3] Bogolyubov N. N., Mitropolskii Yu. A., Asimptoticheskie metody v teorii nelineinykh kolebanii, Nauka, M., 1974 | MR

[4] Ilin A. M., Soglasovanie asimptoticheskikh razlozhenii reshenii kraevykh zadach, Nauka, M, 1989 | MR

[5] Ilin A. M., “O metode dvukh masshtabov v zadache o vozmuschenii odnochastotnogo kolebaniya”, Teor. i matem. fiz., 118:3 (1999), 383–389 | MR

[6] Kalyakin L. A., “Asimptoticheskii analiz modeli avtorezonansa”, Dokl. RAN., 378:5 (2001), 594–597 | MR | Zbl

[7] Kalyakin L. A., “Avtorezonans v dinamicheskoi sisteme”, Sovrem. mat. i eë pril., 5 (2003), 79–108

[8] Kaplan A. E., Kravtsov Yu. A., Rylov V. A., Parametricheskie generatory i deliteli chastoty, Sovetskoe radio, M., 1966

[9] Laricheva V. V., “O rasshirenii intervala primenimosti osredneniya”, DAN SSSR, 220:4 (1975), 775–778 | Zbl

[10] Mitropolskii Yu. A., Khoma G. P., Matematicheskoe obosnovanie asimptoticheskikh metodov nelineinoi mekhaniki., Naukova dumka, Kiev, 1983 | MR

[11] Naife A. Kh., Metody vozmuschenii, Mir, M., 1976 | MR

[12] Naugolnykh K. A., Ostrovskii L. A., Nelineinye volnovye protsessy v akustike, ed. A. V. Gaponova-Grekhova, Nauka, M., 1990 | MR

[13] Nekhoroshev N. N., “Eksponentsialnaya otsenka vremeni ustoichivosti gamiltonovykh sistem, blizkikh k integriruemym”, Uspekhi mat. nauk., 32:6 (1977), 5–66 | MR | Zbl

[14] Nekhoroshev N. N., “Eksponentsialnaya otsenka vremeni ustoichivosti gamiltonovykh sistem, blizkikh k integriruemym. II”, Tr. seminara im. I. G. Petrovskogo, no. 5, 1979, 5–50 | MR | Zbl

[15] Ablowitz M. J., Funk B. A., Newell A. C., “Semi-resonant interactions and frequency dividers”, Stud. Appl. Math., 52:1 (1973), 51–74 | Zbl

[16] Kalyakin L. A., “Justification of asymptotic expansions for the principal resonance equations”, Proc. Steklov Inst. Math., 1, 2003, S108–S122 | MR | Zbl