Geodesic
Adiabatic approximations for Landau–Lifshitz equations
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 13 (2007) no. 2, pp. 104-119 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

The asymptotics with respect to a small parameter for solutions of a system of Landau–Lifshitz equations with slowly varying coefficients and small dissipative terms is investigated. These equations are a mathematical model of a uniaxial ferromagnet in a time-dependent magnetic field. The asymptotics constructed make it possible to describe the magnetization reversal effect and to reveal the influence of the parameters of the external magnetic field and dissipation on the stability of this process. 
@article{TIMM_2007_13_2_a9,
     author = {L. A. Kalyakin and M. A. Shamsutdinov},
     title = {Adiabatic approximations for {Landau{\textendash}Lifshitz} equations},
     journal = {Trudy Instituta matematiki i mehaniki},
     pages = {104--119},
     year = {2007},
     volume = {13},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMM_2007_13_2_a9/}
}
TY  - JOUR
AU  - L. A. Kalyakin
AU  - M. A. Shamsutdinov
TI  - Adiabatic approximations for Landau–Lifshitz equations
JO  - Trudy Instituta matematiki i mehaniki
PY  - 2007
SP  - 104
EP  - 119
VL  - 13
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/TIMM_2007_13_2_a9/
LA  - ru
ID  - TIMM_2007_13_2_a9
ER  - 
%0 Journal Article
%A L. A. Kalyakin
%A M. A. Shamsutdinov
%T Adiabatic approximations for Landau–Lifshitz equations
%J Trudy Instituta matematiki i mehaniki
%D 2007
%P 104-119
%V 13
%N 2
%U http://geodesic.mathdoc.fr/item/TIMM_2007_13_2_a9/
%G ru
%F TIMM_2007_13_2_a9
L. A. Kalyakin; M. A. Shamsutdinov. Adiabatic approximations for Landau–Lifshitz equations. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 13 (2007) no. 2, pp. 104-119. http://geodesic.mathdoc.fr/item/TIMM_2007_13_2_a9/

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

[2] Landau L. D., Lifshitz E. M., “Theory of dispersion of magnetic permeability in ferromagnetic bodies”, Phys. Zs. Sowjetunion, 8:2 (1935), 153–172

[3] Monosov Ya. A., Nelineinyi ferromagnitnyi rezonans, Nauka, M., 1971

[4] Krupicka S., Physik der Ferrite und der verwandten magnetischen Oxide, Academia, Praga, 1973

[5] Gurevich A. V., Melkov G. A., Magnitnye kolebaniya i volny, Nauka, M., 1994 | Zbl

[6] Stoner E. C., Wohlfarth E. P., “A mechanism of magnetic hysteresis in heterogeneous alloys”, Phil. Trans. R. Soc., 240 (1948), 599–642 | DOI

[7] Kuzmak G. E., “Asimptoticheskie resheniya nelineinykh differentsialnykh uravnenii s peremennymi koeffitsientami”, Prikl. matematika i mekhanika, 23:3 (1951), 519–526

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

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

[10] Zaslavskii G. M., Sagdeev R. Z., Vvedenie v nelineinuyu fiziku. Ot mayatnika do turbulentnosti i khaosa, Nauka, M., 1977 | MR

[11] Neishtadt A. I., “Prokhozhdenie cherez separatrisu v rezonansnoi zadache s medlenno izmenyayuschimsya parametrom”, Prikl. matematika i mekhanika, 39:4 (1975), 621–632 | MR