Geodesic
Fundamental mathematical structures of integrable models
Teoretičeskaâ i matematičeskaâ fizika, Tome 118 (1999) no. 3, pp. 405-412 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We consider integrable models in a totally discrete multidimensional space–time. Dynamic variables are associated with cells into which the space is decomposed by a set of intersecting hyperplanes. We investigate the $(2+1)$-dimensional model related to the functional tetrahedron equation. We propose a method for constructing solutions of analogous models in higher dimensions. 
@article{TMF_1999_118_3_a10,
     author = {I. G. Korepanov},
     title = {Fundamental mathematical structures of integrable models},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {405--412},
     year = {1999},
     volume = {118},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1999_118_3_a10/}
}
TY  - JOUR
AU  - I. G. Korepanov
TI  - Fundamental mathematical structures of integrable models
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1999
SP  - 405
EP  - 412
VL  - 118
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/TMF_1999_118_3_a10/
LA  - ru
ID  - TMF_1999_118_3_a10
ER  - 
%0 Journal Article
%A I. G. Korepanov
%T Fundamental mathematical structures of integrable models
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1999
%P 405-412
%V 118
%N 3
%U http://geodesic.mathdoc.fr/item/TMF_1999_118_3_a10/
%G ru
%F TMF_1999_118_3_a10
I. G. Korepanov. Fundamental mathematical structures of integrable models. Teoretičeskaâ i matematičeskaâ fizika, Tome 118 (1999) no. 3, pp. 405-412. http://geodesic.mathdoc.fr/item/TMF_1999_118_3_a10/

[1] C. N. Yang, Phys. Rev. Lett., 19 (1967), 1312–1314 ; R. J. Baxter, Ann. Phys., 70 (1972), 193–228 ; L. D. Faddeev, Sov. Sci. Rev. C, 1 (1980), 107–155 | DOI | MR | DOI | MR | Zbl | Zbl

[2] R. M. Kashaev, Chastnoe soobschenie, 1998

[3] R. M. Kashaev, I. G. Korepanov, S. M. Sergeev, TMF, 117 (1998), 370–384 | DOI | MR | Zbl

[4] R. M. Kashaev, S. M. Sergeev, On pentagon, ten-term, and tetrahedron relations, Preprint ENSLAPP-L-611/96, ENS-Lyon, Lyon, 1996 ; Commun. Math. Phys. (to appear) | MR

[5] S. M. Sergeev, Lett. Math. Phys., 45:2 (1998), 113–119 | DOI | MR | Zbl

[6] T. Miwa, Proc. Japan Acad. Ser. A, 58 (1982), 9–12 | DOI | MR | Zbl

[7] R. Hirota, J. Phys. Soc. Japan, 50:11 (1981), 3785–3791 | DOI | MR

[8] R. M. Kashaev, Lett. Math. Phys., 35 (1996), 389–397 | DOI | MR

[9] N. Shinzawa, S. Saito, A symmetric generalization of linear Bäcklund transformation associated with the Hirota bilinear difference equation, , 1998 E-print solv-int/9801002 | MR

[10] I. G. Korepanov, Integriruemye sistemy v diskretnom prostranstve-vremeni i neodnorodnye modeli dvumernoi statisticheskoi fiziki, Diss. na soiskanie uch. st. dokt. fiz.-mat. nauk, POMI, Sankt-Peterburg, 1995 | Zbl