Geodesic
Solutions of the Periodic Toda Lattice by the Projection and the Algebraic-Geometric Methods
Teoretičeskaâ i matematičeskaâ fizika, Tome 128 (2001) no. 3, pp. 461-473
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We compare different ways to construct solutions of the periodic Toda lattice. We give two recipes that follow from the projection method and compare them with the algebraic-geometric construction of Krichever. 
@article{TMF_2001_128_3_a10,
     author = {M. A. Olshanetsky},
     title = {Solutions of the {Periodic} {Toda} {Lattice} by the {Projection} and the {Algebraic-Geometric} {Methods}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {461--473},
     year = {2001},
     volume = {128},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2001_128_3_a10/}
}
TY  - JOUR
AU  - M. A. Olshanetsky
TI  - Solutions of the Periodic Toda Lattice by the Projection and the Algebraic-Geometric Methods
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2001
SP  - 461
EP  - 473
VL  - 128
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/TMF_2001_128_3_a10/
LA  - ru
ID  - TMF_2001_128_3_a10
ER  - 
%0 Journal Article
%A M. A. Olshanetsky
%T Solutions of the Periodic Toda Lattice by the Projection and the Algebraic-Geometric Methods
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2001
%P 461-473
%V 128
%N 3
%U http://geodesic.mathdoc.fr/item/TMF_2001_128_3_a10/
%G ru
%F TMF_2001_128_3_a10
M. A. Olshanetsky. Solutions of the Periodic Toda Lattice by the Projection and the Algebraic-Geometric Methods. Teoretičeskaâ i matematičeskaâ fizika, Tome 128 (2001) no. 3, pp. 461-473. http://geodesic.mathdoc.fr/item/TMF_2001_128_3_a10/

[1] M. Olshanetsky, A. Perelomov, Lett. Nouvo Cim., 16 (1976), 333 | DOI | MR

[2] M. Olshanetsky, A. Perelomov, Lett. Nouvo Cim., 17 (1976), 97 | DOI | MR

[3] D. Kazdan, B. Kostant, and S. Sternberg, Commun. Pure Appl. Math., 31 (1978), 481–507 | DOI | MR

[4] M. Olshanetsky, A. Perelomov, Invent. Math., 54 (1979), 261–269 | DOI | MR | Zbl

[5] B. Kostant, Adv. in Math., 34 (1979), 195–338 | DOI | MR | Zbl

[6] A. Gorsky, N. Nekrasov, Elliptic Calogero–Moser system from two dimensional current algebra, E-print hep-th/9401021

[7] N. Nekrasov, Commun. Math. Phys., 180 (1996), 587–604 | DOI | MR

[8] N. Hitchin, Duke Math. J., 54 (1987), 91–114 | DOI | MR | Zbl

[9] B. A. Dubrovin, I. M. Krichever, S. P. Novikov, Metody algebraicheskoi i topologicheskoi geometrii v sovremennoi matematicheskoi fizike, 2, Obzory po matematicheskoi fizike, 3, ed. S. P. Novikov, 1990

[10] I. Krichever, O. Babelon, E. Billey, and M. Talon, Spin generalization of the Calogero–Moser system and the Matrix KP equation, E-print hep-th/9411160 | MR

[11] I. Krichever, K. Vaninsky, The periodic and open Toda lattice, E-print hep-th/0010184 | MR

[12] M. Olshanetsky, A. Perelomov, Phys. Rep., 71 (1981), 313–400 | DOI | MR

[13] E. Pressli, G. Sigal, Gruppy petel, Mir, M., 1990 | MR

[14] K. Ueno, K. Takasaki, Proc. Japan Acad., Ser. A, 59 (1983), 167–170 | DOI | MR | Zbl

[15] K. Takasaki, Adv. Stud. Pure Math., 4 (1984), 139–163 | MR | Zbl

[16] A. Reiman, M. Semenov-Tyan-Shanskii, “Teoretiko-gruppovye metody v teorii integriruemykh sistem”, Dinamicheskie sistemy – 7, Itogi nauki i tekhniki. Sovremennye problemy matematiki. Fundamentalnye napravleniya, 16, ed. R. V. Gamkrelidze, VINITI, M., 1987, 119–194 | MR | Zbl