Geodesic
On some generalizations of the factorization method
Teoretičeskaâ i matematičeskaâ fizika, Tome 110 (1997) no. 3, pp. 339-350 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The classical factorization method reduces the system of differential equations $U_t=[U_+,U]$ to the problem of solving algebraic equations. Here $U(t)$ belongs to a Lie algebra $\mathfrak G$ which is the direct sum of subalgebras $\mathfrak G_+$ and $\mathfrak G_-$, where “+” denotes the projection on $\mathfrak G_+$. This method is generalized to the case $\mathfrak G_+\cap\mathfrak G_-\ne\{0\}$. The corresponding quadratic systems are reduced to linear systems with varying coefficients. It is shown that the generalized version of the factorization method is also applicable to systems of partial differential equations of the Liouville type equation. 
@article{TMF_1997_110_3_a0,
     author = {I. Z. Golubchik and V. V. Sokolov},
     title = {On some generalizations of the factorization method},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {339--350},
     year = {1997},
     volume = {110},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1997_110_3_a0/}
}
TY  - JOUR
AU  - I. Z. Golubchik
AU  - V. V. Sokolov
TI  - On some generalizations of the factorization method
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1997
SP  - 339
EP  - 350
VL  - 110
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/TMF_1997_110_3_a0/
LA  - ru
ID  - TMF_1997_110_3_a0
ER  - 
%0 Journal Article
%A I. Z. Golubchik
%A V. V. Sokolov
%T On some generalizations of the factorization method
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1997
%P 339-350
%V 110
%N 3
%U http://geodesic.mathdoc.fr/item/TMF_1997_110_3_a0/
%G ru
%F TMF_1997_110_3_a0
I. Z. Golubchik; V. V. Sokolov. On some generalizations of the factorization method. Teoretičeskaâ i matematičeskaâ fizika, Tome 110 (1997) no. 3, pp. 339-350. http://geodesic.mathdoc.fr/item/TMF_1997_110_3_a0/

[1] B. Konstant, Lect. Notes Ser., 34, 1979, 287–316

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

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

[4] I. Z. Golubchik, V. V. Sokolov, S. I. Svinolupov, A new class of nonassociative algebras and a generalized factorization method, Preprint ESI 53, Wien (Austria), 1993

[5] O. I. Bogoyavlenskii, Oprokidyvayuschiesya solitony, Nauka, M., 1991 | MR