Geodesic
Averaging of the Bloch equations
Vestnik Chelyabinskogo Gosudarstvennogo Universiteta. Matematika, Mekhanika, Informatika, no. 14 (2011), pp. 107-112 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The system of three first-order differential equations with weakly varying coefficients, which is refered as the Bloch equations in the theory of nuclear magnetization is considered. Averaging of the system is performed by using the equations with both frozen coefficients and zero dissipation.
Keywords: small parameter, averaging, nonlinear equation. 
@article{VCHGU_2011_14_a10,
     author = {O. A. Sultanov and L. A. Kalyakin},
     title = {Averaging of the {Bloch} equations},
     journal = {Vestnik Chelyabinskogo Gosudarstvennogo Universiteta. Matematika, Mekhanika, Informatika},
     pages = {107--112},
     year = {2011},
     number = {14},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VCHGU_2011_14_a10/}
}
TY  - JOUR
AU  - O. A. Sultanov
AU  - L. A. Kalyakin
TI  - Averaging of the Bloch equations
JO  - Vestnik Chelyabinskogo Gosudarstvennogo Universiteta. Matematika, Mekhanika, Informatika
PY  - 2011
SP  - 107
EP  - 112
IS  - 14
UR  - http://geodesic.mathdoc.fr/item/VCHGU_2011_14_a10/
LA  - ru
ID  - VCHGU_2011_14_a10
ER  - 
%0 Journal Article
%A O. A. Sultanov
%A L. A. Kalyakin
%T Averaging of the Bloch equations
%J Vestnik Chelyabinskogo Gosudarstvennogo Universiteta. Matematika, Mekhanika, Informatika
%D 2011
%P 107-112
%N 14
%U http://geodesic.mathdoc.fr/item/VCHGU_2011_14_a10/
%G ru
%F VCHGU_2011_14_a10
O. A. Sultanov; L. A. Kalyakin. Averaging of the Bloch equations. Vestnik Chelyabinskogo Gosudarstvennogo Universiteta. Matematika, Mekhanika, Informatika, no. 14 (2011), pp. 107-112. http://geodesic.mathdoc.fr/item/VCHGU_2011_14_a10/

[1] A. S. Borovik-Romanov i dr., “Spinovoe ekho v sistemakh so svyazannoi yaderno-elektronnoi pretsessiei”, Uspekhi fiz. nauk, 142:4 (1984), 537–570

[2] L. A. Kalyakin, O. A. Sultanov, M. A. Shamsutdinov, “Asimptoticheskii analiz modeli yadernogo magnitnogo avtorezonansa”, Teoret. i mat. fizika, 167:3 (2011), 419–430

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

[4] V. V. Nemytskii, V. V. Stepanov, Kachestvennaya teoriya differentsialnykh uravnenii, Editorial URSS, M., 2004, 552 pp.

[5] R. Z. Khasminskii, Ustoichiovst sistem differentsialnykh uravnenii pri sluchainykh vozmuscheniyakh ikh parametrov, Nauka, M., 1969, 368 pp.

[6] V. D. Azhotkin, V. M. Babich, “O primenenii metoda dvukhmasshtabnykh razlozhenii k odnochastotnoi zadache teorii nelineinykh kolebanii”, Priklad. matematika i mekhanika, 49:3 (1985), 377–383