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TMF, 2012, Volume 172, Number 3, Pages 387–402 (Mi tmf6960)  

This article is cited in 6 scientific papers (total in 6 papers)

Semidiscrete Toda lattices

S. V. Smirnov

Lomonosov Moscow State University, Moscow, Russia

Abstract: 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

DOI: https://doi.org/10.4213/tmf6960

Full text: PDF file (481 kB)
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English version:
Theoretical and Mathematical Physics, 2012, 172:3, 1217–1231

Bibliographic databases:

Received: 13.01.2012

Citation: S. V. Smirnov, “Semidiscrete Toda lattices”, TMF, 172:3 (2012), 387–402; Theoret. and Math. Phys., 172:3 (2012), 1217–1231

Citation in format AMSBIB
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  • https://doi.org/10.4213/tmf6960
  • http://mi.mathnet.ru/eng/tmf/v172/i3/p387

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. S. V. Smirnov, “Darboux integrability of discrete two-dimensional Toda lattices”, Theoret. and Math. Phys., 182:2 (2015), 189–210  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    2. Ismagil Habibullin, Mariya Poptsova, “Classification of a Subclass of Two-Dimensional Lattices via Characteristic Lie Rings”, SIGMA, 13 (2017), 073, 26 pp.  mathnet  crossref
    3. S.-Q. Liu, Y. Zhang, Ch. Zhou, “Fractional Volterra hierarchy”, Lett. Math. Phys., 108:2 (2018), 261–283  crossref  mathscinet  zmath  isi
    4. M. N. Poptsova, I. T. Habibullin, “Algebraic properties of quasilinear two-dimensional lattices connected with integrability”, Ufa Math. J., 10:3 (2018), 86–105  mathnet  crossref  isi
    5. S. V. Smirnov, “Factorization of Darboux–Laplace transformations for discrete hyperbolic operators”, Theoret. and Math. Phys., 199:2 (2019), 621–636  mathnet  crossref  crossref  adsnasa  isi  elib
    6. I. T. Habibullin, M. N. Kuznetsova, “A classification algorithm for integrable two-dimensional lattices via Lie–Rinehart algebras”, Theoret. and Math. Phys., 203:1 (2020), 569–581  mathnet  crossref  crossref  isi  elib
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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