Geodesic
Semidiscrete Toda lattices
Teoretičeskaâ i matematičeskaâ fizika, Tome 172 (2012) no. 3, pp. 387-402

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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},
     publisher = {mathdoc},
     volume = {172},
     number = {3},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2012_172_3_a4/}
}
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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/