Geodesic
Matrix functional substitutions for integrable dynamical systems and the Landau–Lifshitz equations
Russian journal of nonlinear dynamics, Tome 10 (2014) no. 1, pp. 35-48

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

The paper sets out the main elements of the theory of matrix functional substitutions to the construction of integrable finite-dimensional dynamical systems and the application of this theory to the integration of the Landau–Lifshitz equation for a homogeneous magnetic field in the external variable fields. Developed a general scheme for constructing solutions and is an example of the construction of the exact solution for a circularly polarized field.
Keywords: integrable finite-dimensional dynamical systems, matrix functional substitutions, Landau–Lifshitz equations. 
Victor M. Zhuravlev. Matrix functional substitutions for integrable dynamical systems and the Landau–Lifshitz equations. Russian journal of nonlinear dynamics, Tome 10 (2014) no. 1, pp. 35-48. http://geodesic.mathdoc.fr/item/ND_2014_10_1_a2/
@article{ND_2014_10_1_a2,
     author = {Victor M. Zhuravlev},
     title = {Matrix functional substitutions for integrable dynamical systems and the {Landau{\textendash}Lifshitz} equations},
     journal = {Russian journal of nonlinear dynamics},
     pages = {35--48},
     year = {2014},
     volume = {10},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ND_2014_10_1_a2/}
}
TY  - JOUR
AU  - Victor M. Zhuravlev
TI  - Matrix functional substitutions for integrable dynamical systems and the Landau–Lifshitz equations
JO  - Russian journal of nonlinear dynamics
PY  - 2014
SP  - 35
EP  - 48
VL  - 10
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/ND_2014_10_1_a2/
LA  - ru
ID  - ND_2014_10_1_a2
ER  - 
%0 Journal Article
%A Victor M. Zhuravlev
%T Matrix functional substitutions for integrable dynamical systems and the Landau–Lifshitz equations
%J Russian journal of nonlinear dynamics
%D 2014
%P 35-48
%V 10
%N 1
%U http://geodesic.mathdoc.fr/item/ND_2014_10_1_a2/
%G ru
%F ND_2014_10_1_a2

[1] Zakharov V. E., Manakov S. V., Novikov S. P., Pitaevskii L. P., Teoriya solitonov i metod obratnoi zadachi rasseyaniya, Nauka, M., 1980, 319 pp. | MR

[2] Dodd R., Eilbek Dzh., Gibbon Dzh., Solitony i nelineinye volnovye uravneniya, Mir, M., 1988, 694 pp. | MR

[3] Zhuravlev V. M., Nikitin A. V., “Novyi podkhod k postroeniyu nelineinykh evolyutsionnykh uravnenii, linearizuemykh s pomoschyu podstanovok tipa Koula–Khopfa”, Nelineinyi mir, 5:9 (2007), 603–611

[4] Zhuravlev V. M., “Metod obobschennykh podstanovok Koula–Khopfa i novye primery linearizuemykh nelineinykh evolyutsionnykh uravnenii”, TMF, 158:1 (2009), 58–71 | DOI | MR | Zbl

[5] Zhiber A. V., Murtazina R. D., Khabibullin I. T., Shabat A. B., “Kharakteristicheskie koltsa Li i integriruemye modeli matematicheskoi fiziki”, Ufimsk. matem. zhurn., 4:3 (2012), 17–85

[6] Borisov A. V., Mamaev I. S., Dinamika tverdogo tela, NITs «RKhD», Izhevsk, 2001, 384 pp. | MR | Zbl

[7] Zhuravlev V. M., Obrubov K. S., “Metod obobschennykh podstanovok Koula–Khopfa v teorii konechnomernykh nelineinykh dinamicheskikh sistem”, Vestn. Sam. gos. tekhn. un-ta. Ser. fiz.-mat. nauki, 2011, no. 1(22), 83–89 | DOI | MR

[8] Gurevich A. G., Magnitnyi rezonans v ferritakh i antiferromagnetikakh, Nauka, M., 1973, 592 pp.

[9] Gurevich A. G., Melkov G. A., Magnitnye kolebaniya i volny, Fizmatlit, M., 1973, 464 pp.

[10] Sokhotskii G. V., “Esche raz ob uravnenii Landau–Lifshitsa”, UFN, 144:4 (1984), 681–686 | DOI

[11] Shamsutdinov M. A., Kalyakin L. A., Kharisov A. T., “Avtorezonans v ferromagnitnoi plenke”, ZhTF, 80:6 (2010), 106–111

[12] Sementsov D. I., Shutyi A. M., “Nelineinaya regulyarnaya dinamika i stokhasticheskaya dinamika v tonkoplenochnykh strukturakh”, UFN, 177:8 (2007), 831–857 | DOI