Geodesic
Factorization of loop algebras over $\mathrm{so}(4)$ and integrable nonlinear differential equations
Fundamentalʹnaâ i prikladnaâ matematika, Tome 11 (2005) no. 3, pp. 79-94.

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

We consider factoring subalgebras for loop algebras over $\mathrm{so}(4)$. Given a factoring subalgebra, we find (in terms of coefficients of commutator relations) an explicit form of (1) the corresponding system of the chiral field equation type, (2) the corresponding two-spin model of the Landau–Lifshitz equation, and (3) the corresponding Hamiltonian system of ordinary differential equations with homogeneous quadratic Hamiltonian and linear $\mathrm{so}(4)$-Poisson brackets. 
@article{FPM_2005_11_3_a4,
     author = {O. V. Efimovskaya},
     title = {Factorization of loop algebras over $\mathrm{so}(4)$ and integrable nonlinear differential equations},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {79--94},
     publisher = {mathdoc},
     volume = {11},
     number = {3},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2005_11_3_a4/}
}
TY  - JOUR
AU  - O. V. Efimovskaya
TI  - Factorization of loop algebras over $\mathrm{so}(4)$ and integrable nonlinear differential equations
JO  - Fundamentalʹnaâ i prikladnaâ matematika
PY  - 2005
SP  - 79
EP  - 94
VL  - 11
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/FPM_2005_11_3_a4/
LA  - ru
ID  - FPM_2005_11_3_a4
ER  - 
%0 Journal Article
%A O. V. Efimovskaya
%T Factorization of loop algebras over $\mathrm{so}(4)$ and integrable nonlinear differential equations
%J Fundamentalʹnaâ i prikladnaâ matematika
%D 2005
%P 79-94
%V 11
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/FPM_2005_11_3_a4/
%G ru
%F FPM_2005_11_3_a4
O. V. Efimovskaya. Factorization of loop algebras over $\mathrm{so}(4)$ and integrable nonlinear differential equations. Fundamentalʹnaâ i prikladnaâ matematika, Tome 11 (2005) no. 3, pp. 79-94. http://geodesic.mathdoc.fr/item/FPM_2005_11_3_a4/

[1] Golod P. I., “Gamiltonovy sistemy na orbitakh affinnykh grupp Li i nelineinye integriruemye uravneniya”, Fizika mnogochastichnykh sistem, t. 7, Naukova Dumka, Kiev, 1985, 30–39 | MR

[2] Golubchik I. Z., Sokolov V. V., “Obobschënnye uravneniya Gaizenberga na $\mathbb Z$-graduirovannykh algebrakh Li”, Teor. i matem. fiz., 120:2 (1999), 248–255 | MR | Zbl

[3] Golubchik I. Z., Sokolov V. V., “Soglasovannye skobki Li i integriruemye uravneniya tipa modeli glavnogo kiralnogo polya”, Funktsion. analiz i ego pril., 36:3 (2002), 9–19 | MR | Zbl

[4] Golubchik I. Z., Sokolov V. V., “Faktorizatsiya algebry petel i integriruemye uravneniya tipa volchkov”, Teor. i matem. fiz., 141:1 (2004), 3–23 | MR | Zbl

[5] Dubrovin B. A., Krichever I. M., Novikov S. P., “Integriruemye sistemy”, Itogi nauki i tekhn. Ser. Sovr. probl. matematiki. Fundamentalnye napravleniya, 4, VINITI, M., 1985, 179–284 | MR

[6] Dubrovin B. A., Novikov S. P., Matveev V. B., “Nelineinye uravneniya tipa Kortevega–de Friza, konechnozonnye lineinye operatory i abelevy mnogoobraziya”, Uspekhi mat. nauk, 31:1 (1976), 55–136 | MR | Zbl

[7] Efimovskaya O. V., Sokolov V. V., “Razlozheniya algebry petel nad $\mathrm{so}(4)$ i integriruemye modeli tipa uravneniya kiralnogo polya”, Fundam. i prikl. mat., 10:1 (2004), 39–47 | MR | Zbl

[8] Zakharov V. E., Manakov S. V., Novikov S. P., Pitaevskii L. P., Teoriya solitonov: metod obratnoi zadachi, Nauka, M., 1980 | MR

[9] Reiman A. G., Semënov-tyan-Shanskii M. A., Integriruemye sistemy. Teoretiko-gruppovoi podkhod, RKhD, Izhevsk, 2003

[10] Semënov-Tyan-Shanskii M. A., “Chto takoe klassicheskaya $r$-matritsa”, Funktsion. analiz i ego pril., 17:4 (1983), 17–33 | MR

[11] Sokolov V. V., “O razlozheniyakh algebry petel nad $\mathrm{so}(3)$ v summu dvukh podalgebr”, Dokl. RAN, 397:3 (2004), 321–324 | MR

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

[13] Cherednik I. V., “Funktsionalnye realizatsii bazisnykh predstavlenii faktorizuyuschikh grupp i algebr Li”, Funktsion. analiz i ego pril., 19:3 (1985), 36–52 | MR | Zbl

[14] Golubchik I. Z., Sokolov V. V., “Factorization of the loop algebras and compatible Lie brackets”, J. Nonlinear Math. Phys., 12:1 (2005), 343–350 | DOI | MR

[15] Lax P. D., “Integrals of nonlinear equations of evolution and solitary waves”, Comm. Pure Appl. Math., 21:5 (1968), 467–490 | DOI | MR | Zbl