Geodesic
Jordan algebras and generalized Korteweg–de Vries equations
Teoretičeskaâ i matematičeskaâ fizika, Tome 87 (1991) no. 3, pp. 391-403 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Integrability criteria for many-field Korteweg–de Vries equations are obtained. A one-to-one correspondence between such equations and Jordan algebras is established. It is shown that the so-called irreducible systems correspond to simple Jordan algebras. 
@article{TMF_1991_87_3_a2,
     author = {S. I. Svinolupov},
     title = {Jordan algebras and generalized {Korteweg{\textendash}de~Vries} equations},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {391--403},
     year = {1991},
     volume = {87},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1991_87_3_a2/}
}
TY  - JOUR
AU  - S. I. Svinolupov
TI  - Jordan algebras and generalized Korteweg–de Vries equations
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1991
SP  - 391
EP  - 403
VL  - 87
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/TMF_1991_87_3_a2/
LA  - ru
ID  - TMF_1991_87_3_a2
ER  - 
%0 Journal Article
%A S. I. Svinolupov
%T Jordan algebras and generalized Korteweg–de Vries equations
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1991
%P 391-403
%V 87
%N 3
%U http://geodesic.mathdoc.fr/item/TMF_1991_87_3_a2/
%G ru
%F TMF_1991_87_3_a2
S. I. Svinolupov. Jordan algebras and generalized Korteweg–de Vries equations. Teoretičeskaâ i matematičeskaâ fizika, Tome 87 (1991) no. 3, pp. 391-403. http://geodesic.mathdoc.fr/item/TMF_1991_87_3_a2/

[1] Athorne C., Fordy A., J. Phys. A, 20 (1987), 1377–1386 | DOI | MR | Zbl

[2] Drinfeld V. G., Sokolov V. V., Sovremennye problemy matematiki, 24, VINITI, M., 1984, 81–180 | MR | Zbl

[3] Jacobson N., Structure and representations of Jordan algebras, Providence, 1968 | MR

[4] Jordan P., von Neumann J., Wigner E., Ann. of Math., 36 (1934), 29–64 | DOI

[5] Slinko A. M., Shestakov I. P., Shirshov A. I., Koltsa, blizkie k assotsiativnym, Nauka, M., 1978 | MR | Zbl

[6] Mikhailov A. V., Shabat A. B., Yamilov R. I., UMN, 42:4 (1987), 3–53 | MR

[7] Mikhailov A. V., Sokolov V. V., Shabat A. B., “Simmetriinyi podkhod k klassifikatsii integriruemykh uravnenii”, Integriruemost i kineticheskie uravneniya dlya solitonov, Naukova dumka, Kiev, 1989

[8] Olver P., Prilozheniya grupp Li k differentsialnym uravneniyam, Mir, M., 1989 | MR | Zbl

[9] Albert A., Ann. Math., 48 (1947), 546–567 | DOI | MR | Zbl

[10] Albert A., Trans. Amer. Math. Soc., 69 (1950), 503–527 | DOI | MR | Zbl