Geodesic
Hamiltonian structures for integrable field theory models. II. Models with $O(n)$ and $Sp(2k)$ symmetry on a one-dimensional lattice
Teoretičeskaâ i matematičeskaâ fizika, Tome 63 (1985) no. 2, pp. 197-207 
N. Yu. Reshetikhin. Hamiltonian structures for integrable field theory models. II. Models with $O(n)$ and $Sp(2k)$ symmetry on a one-dimensional lattice. Teoretičeskaâ i matematičeskaâ fizika, Tome 63 (1985) no. 2, pp. 197-207. http://geodesic.mathdoc.fr/item/TMF_1985_63_2_a3/
@article{TMF_1985_63_2_a3,
     author = {N. Yu. Reshetikhin},
     title = {Hamiltonian structures for integrable field theory models. {II.~Models} with $O(n)$ and $Sp(2k)$ symmetry on a~one-dimensional lattice},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {197--207},
     year = {1985},
     volume = {63},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1985_63_2_a3/}
}
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A new family of classical integrable systems with $O(n)$ and $Sp(2k)$ symmetry is found. It is shown that these systems can be regarded as lattice analogs of models of the nonlinear Schrödinger equation on symmetric spaces. An example of a $O(n)$-invariant classical discrete magnet with local Hamiltonian is constructed.

[1] Sklyanin E. K., Zap. nauch. semin. LOMI, 95, 1980, 55–128 | MR | Zbl

[2] Izergin A. G., Korepin V. E., Fizika EChAYa, 13:3, 501–541 | MR

[3] Reshetikhin N. Yu., Faddeev L. D., TMF, 56:3 (1983), 323–343 | MR

[4] Faddeev L. D., Integrable models in $1+1$ dimensional quantum field theory, Preprint S. Ph. T. 182/76, CEN.-SACLAY, 1982 | MR

[5] Belavin A. A., Drinfeld V. G., Funkts. analiz i ego prilozh., 16:3 (1982), 1–29 | MR | Zbl

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

[7] Sklyanin E. K., Funkts. analiz i ego prilozh., 16:4 (1982), 27–34 | MR | Zbl

[8] Sklyanin E. K., Funkts. analiz i ego prilozh., 17:4 (1983), 34–48 | MR | Zbl

[9] Kulish P. P., Reshetikhin N. Yu., Sklyanin E. K., Lett. Math. Phys., 5:5 (1981), 393–403 | DOI | MR | Zbl

[10] Kulish P. P., Reshetikhin N. Yu., Zap. nauch. semin. LOMI, 120, 1982, 92–121 | MR

[11] Babelon O., Representation of the Yang-Baxter algebras associated to Toda field theory, Preprint PAR LPTHE 83M3, May 1983 | MR

[12] Kirillov A. A., Elementy teorii predstavlenii, Nauka, M., 1978, 343 pp. | MR | Zbl

[13] Fordy A. P., Kulish P. P., Commun. Math. Phys., 89 (1983), 427–443 | DOI | MR | Zbl