Geodesic
Classical integrable lattice models through quantum group related formalism
Teoretičeskaâ i matematičeskaâ fizika, Tome 99 (1994) no. 3, pp. 428-434 
A. Kundu. Classical integrable lattice models through quantum group related formalism. Teoretičeskaâ i matematičeskaâ fizika, Tome 99 (1994) no. 3, pp. 428-434. http://geodesic.mathdoc.fr/item/TMF_1994_99_3_a10/
@article{TMF_1994_99_3_a10,
     author = {A. Kundu},
     title = {Classical integrable lattice models through quantum group related formalism},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {428--434},
     year = {1994},
     volume = {99},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1994_99_3_a10/}
}
TY  - JOUR
AU  - A. Kundu
TI  - Classical integrable lattice models through quantum group related formalism
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1994
SP  - 428
EP  - 434
VL  - 99
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/TMF_1994_99_3_a10/
LA  - ru
ID  - TMF_1994_99_3_a10
ER  - 
%0 Journal Article
%A A. Kundu
%T Classical integrable lattice models through quantum group related formalism
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1994
%P 428-434
%V 99
%N 3
%U http://geodesic.mathdoc.fr/item/TMF_1994_99_3_a10/
%G ru
%F TMF_1994_99_3_a10

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

We effectively translate our earlier quantum constructions to the classical language and, using Yang–Baxterisation of the Faddeev–Reshetikhin–Takhtajan algebra, are able to construct the Lax operators and associated $r$-matrices of classical integrable models. Thus, new as well as known lattice systems of different classes are generated, including new types of collective integrable models and canonical models with nonstandard $r$ matrices.

[1] A. Kundu, B. Basumallick, Mod. Phys. Lett. A, 7 (1992), 61 ; Coloured FRT algebra and its Yang-Baxterisation leading to integrable models with nonadditive $R$-matrix, Saha Inst. Preprint, april 1993 | DOI | MR | Zbl

[2] N. Yu. Reshitikhin, L. A. Takhtajan, L. D. Faddeev, Algebra and Analysis, 1 (1989), 17

[3] M. J. Ablowitz, J. F. Ladik, Stud. Appl. Math., 55 (1976), 213 | DOI | MR | Zbl

[4] Yu. B. Suris, Phys. Lett. A, 145 (1990), 113 | DOI | MR

[5] I. Mirola, O. Ragnisco, T. G. Zhang, A novel hierarchy of integrable lattices, Rome Univ. Preprint No 976, 1993 | MR

[6] V. F. R. Jones, Int. J. Mod. Phys. B, 4 (1993), 701 | DOI | MR

[7] M. Jimbo, Lett. Math. Phys., 20 (1985), 331 ; V. G. Drinfeld, Proc. ICM, Berkeley, 1986, 798 | MR

[8] A. G. Izergin, V. E. Korepin, Nucl. Phys. B, 205 (1982), 401 | DOI | MR

[9] A. G. Izergin, V. E. Korepin, Sov. Phys. Dokl., 259 (1981), 76 ; V. O. Tarasov, L. A. Takhtajan, L. D. Faddeev, Teor. Mat. Fiz., 57 (1983), 163 | MR | Zbl | DOI | MR

[10] P. L. Christiansen, M. F. Jorgensen, V. B. Kuznetsov, Lett. Math. Phys., 29 (1993), 165 | DOI | MR | Zbl

[11] O. Ragnisco, A. Kundu, A simple lattice variant of NLS equation and its deformation with exact quantum solution, Saha Inst. Preprint SINP/TNP/92-15, 1992 | MR

[12] N. Reshetikhin, Lett. Math. Phys., 20 (1990), 331 | DOI | MR | Zbl

[13] A. Kundu, B. Basumallick, J. Math. Phys., 34 (1993), 1052 ; B. Basumallick, A. Kundu, Phys. Lett. B, 287 (1992), 149 | DOI | MR | Zbl | DOI | MR

[14] A. J. MacFarlane, J. Phys. A, 22 (1989), 4581 | DOI | MR | Zbl