Generalized Heisenberg equations on $\mathbb Z$-graded Lie algebras
Teoretičeskaâ i matematičeskaâ fizika, Tome 120 (1999) no. 2, pp. 248-255 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We study the integrable systems of the Heisenberg equation type that correspond to different decompositions of $\mathbb Z$-graded Lie algebras into a direct sum of two subalgebras. We discover new non-Abelian generalizations of some known integrable models.
@article{TMF_1999_120_2_a5,
     author = {I. Z. Golubchik and V. V. Sokolov},
     title = {Generalized {Heisenberg} equations on $\mathbb Z$-graded {Lie} algebras},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {248--255},
     year = {1999},
     volume = {120},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1999_120_2_a5/}
}
TY  - JOUR
AU  - I. Z. Golubchik
AU  - V. V. Sokolov
TI  - Generalized Heisenberg equations on $\mathbb Z$-graded Lie algebras
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1999
SP  - 248
EP  - 255
VL  - 120
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/TMF_1999_120_2_a5/
LA  - ru
ID  - TMF_1999_120_2_a5
ER  - 
%0 Journal Article
%A I. Z. Golubchik
%A V. V. Sokolov
%T Generalized Heisenberg equations on $\mathbb Z$-graded Lie algebras
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1999
%P 248-255
%V 120
%N 2
%U http://geodesic.mathdoc.fr/item/TMF_1999_120_2_a5/
%G ru
%F TMF_1999_120_2_a5
I. Z. Golubchik; V. V. Sokolov. Generalized Heisenberg equations on $\mathbb Z$-graded Lie algebras. Teoretičeskaâ i matematičeskaâ fizika, Tome 120 (1999) no. 2, pp. 248-255. http://geodesic.mathdoc.fr/item/TMF_1999_120_2_a5/

[1] O. I. Mokhov, E. V. Ferapontov, Funkts. analiz i ego prilozh., 28 (1994), 60–63 | MR | Zbl

[2] S. I. Svinolupov, V. V. Sokolov, TMF, 108:3 (1996), 388–392 | DOI | MR | Zbl

[3] I. Z. Golubchik, V. V. Sokolov, TMF, 112:3 (1997), 375–383 | DOI | MR | Zbl

[4] L. A. Takhtadzhyan, L. D. Faddeev, Gamiltonov podkhod v teorii solitonov, Nauka, M., 1986 | MR | Zbl

[5] V. G. Drinfeld, V. V. Sokolov, “Algebry Li i uravneniya tipa Kortevega–de Friza”, Itogi nauki i tekhniki. Sovremennye probl. matematiki. Fundamentalnye napravleniya, 24, VINITI, M., 1984, 81–180 | MR

[6] S. I. Svinolupov, V. V. Sokolov, TMF, 100:2 (1994), 214–218 | MR | Zbl

[7] O. V. Melnikov, V. N. Remeslennikov, V. A. Romankov, L. A. Skornyakov, I. P. Shestakov, Obschaya algebra, T. 1, Nauka, M., 1990 | MR

[8] I. T. Habibullin, V. V. Sokolov, R. I. Yamilov, “Multi-component integrable systems and nonassociative structures”, Nonlinear Physics: Theory and Experiment, eds. E. Alfinito et al., World Scientific Publisher, Singapore, 1996, 139–168 | MR | Zbl

[9] V. Ostapenko, C. R. Acad. Sci. Paris. Ser. I, 315 (1992), 669–673 | MR | Zbl

[10] A. Stolin, Math. Scand., 69 (1991), 57–80 | DOI | MR

[11] A. A. Belavin, V. G. Drinfeld, Funkts. analiz i ego prilozh., 16 (3) (1982), 1–29 | MR | Zbl

[12] M. A. Semenov-Tyan-Shanskii, Funkts. analiz i ego prilozh., 17 (4) (1983), 17–33 | MR