Geodesic
Semidiscrete Toda lattices
Teoretičeskaâ i matematičeskaâ fizika, Tome 172 (2012) no. 3, pp. 387-402 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We study integrable cutoff constraints for a semidiscrete Toda lattice. We construct a Lax representation for a semidiscrete analogue of lattices corresponding to simple Lie algebras of the $C$ series. We introduce nonlocal variables in terms of which the symmetries of the infinite semidiscrete lattice can be expressed, and we classify cutoff constraints of a certain form compatible with the symmetries of the infinite lattice.
Keywords: semidiscrete Toda lattice, Lax representation, symmetry, integrable cutoff constraint. 
@article{TMF_2012_172_3_a4,
     author = {S. V. Smirnov},
     title = {Semidiscrete {Toda} lattices},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {387--402},
     year = {2012},
     volume = {172},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2012_172_3_a4/}
}
TY  - JOUR
AU  - S. V. Smirnov
TI  - Semidiscrete Toda lattices
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2012
SP  - 387
EP  - 402
VL  - 172
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/TMF_2012_172_3_a4/
LA  - ru
ID  - TMF_2012_172_3_a4
ER  - 
%0 Journal Article
%A S. V. Smirnov
%T Semidiscrete Toda lattices
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2012
%P 387-402
%V 172
%N 3
%U http://geodesic.mathdoc.fr/item/TMF_2012_172_3_a4/
%G ru
%F TMF_2012_172_3_a4
S. V. Smirnov. Semidiscrete Toda lattices. Teoretičeskaâ i matematičeskaâ fizika, Tome 172 (2012) no. 3, pp. 387-402. http://geodesic.mathdoc.fr/item/TMF_2012_172_3_a4/

[1] M. Toda, J. Phys. Soc. Jpn., 22:2 (1967), 431–436 | DOI

[2] O. I. Bogoyavlensky, Commun. Math. Phys., 51:3 (1976), 201–209 | DOI | MR

[3] A. V. Mikhailov, Pisma v ZhETF, 30:7 (1979), 443–448

[4] A. N. Leznov, TMF, 42:3 (1980), 343–349 | DOI | MR | Zbl

[5] A. V. Mikhailov, M. A. Olshanetsky, A. M. Perelomov, Commun. Math. Phys., 79:4 (1981), 473–488 | DOI | MR

[6] A. B. Shabat, R. I. Yamilov, Eksponentsialnye sistemy tipa I i matritsy Kartana, Preprint, BFAN SSSR, Ufa, 1981

[7] A. N. Leznov, V. G. Smirnov, A. B. Shabat, TMF, 51:1 (1982), 10–21 | DOI | MR | Zbl

[8] Yu. B. Suris, Algebra i analiz, 2:2 (1990), 141–157 | MR | Zbl

[9] A. B. Shabat, TMF, 103:1 (1995), 170–175 | DOI | MR | Zbl

[10] J. Liouville, J. Math. Pure Appl., 18 (1853)

[11] I. T. Khabibullin, TMF, 143:1 (2005), 33–48 | DOI | MR | Zbl

[12] B. Gürel, I. Habibullin, Phys. Lett. A, 233:1–2 (1997), 68–72 | DOI | MR | Zbl

[13] A. B. Shabat, Phys. Lett. A, 200:2 (1995), 121–133 | DOI | MR | Zbl

[14] V. E. Adler, S. Ya. Startsev, TMF, 121:2 (1999), 271–284 | DOI | MR | Zbl

[15] I. Habibullin, K. Zheltukhin, M. Yangubaeva, J. Phys. A, 44:46 (2011), 465202, 20 pp., arXiv: 1105.4446 | DOI | MR | Zbl