Geodesic
Reductions of the Volterra and Toda chains
Teoretičeskaâ i matematičeskaâ fizika, Tome 124 (2000) no. 3, pp. 419-425 
A. K. Svinin. Reductions of the Volterra and Toda chains. Teoretičeskaâ i matematičeskaâ fizika, Tome 124 (2000) no. 3, pp. 419-425. http://geodesic.mathdoc.fr/item/TMF_2000_124_3_a4/
@article{TMF_2000_124_3_a4,
     author = {A. K. Svinin},
     title = {Reductions of the {Volterra} and {Toda} chains},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {419--425},
     year = {2000},
     volume = {124},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2000_124_3_a4/}
}
TY  - JOUR
AU  - A. K. Svinin
TI  - Reductions of the Volterra and Toda chains
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2000
SP  - 419
EP  - 425
VL  - 124
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/TMF_2000_124_3_a4/
LA  - ru
ID  - TMF_2000_124_3_a4
ER  - 
%0 Journal Article
%A A. K. Svinin
%T Reductions of the Volterra and Toda chains
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2000
%P 419-425
%V 124
%N 3
%U http://geodesic.mathdoc.fr/item/TMF_2000_124_3_a4/
%G ru
%F TMF_2000_124_3_a4

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

We consider Volterra and Toda systems. Using certain algebraic relations, we construct a denumerable class of reductions of these differential–difference systems. The result is given by finite-dimensional systems with Bäcklund autotransformations.

[1] S. V. Manakov, ZhETF, 67 (1974), 543 | MR

[2] M. Toda, Teoriya nelineinykh reshetok, Mir, M., 1984 | MR

[3] M. Toda, Suppl. Progr. Theor. Phys., 59 (1976), 1 | DOI

[4] M. Wadati, Suppl. Progr. Theor. Phys., 59 (1976), 36 | DOI

[5] H. Flaschka, Phys. Rev. B, 9 (1974), 1924 | DOI | MR | Zbl

[6] H. Flaschka, Progr. Theor. Phys., 51 (1974), 703 | DOI | MR | Zbl

[7] D. Levi, J. Phys. A, 14 (1981), 1083 | DOI | MR | Zbl

[8] A. N. Leznov, A. B. Shabat, R. I. Yamilov, Phys. Lett. A, 174 (1993), 397 | DOI | MR

[9] H. Aratyn, L. A. Ferreira, J. F. Gomez, A. H. Zimerman, Toda and Volterra lattice equations from discrete symmetries of KP hierarchies, E-print hep-th/9307147 | MR

[10] J. Liouville, J. Math. Pure Appl., 20 (1855), 137

[11] V. I. Arnold, Matematicheskie metody klassicheskoi mekhaniki, Nauka, M., 1989 | MR