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TMF, 2004, Volume 138, Number 3, Pages 422–436 (Mi tmf30)  

This article is cited in 4 scientific papers (total in 4 papers)

Finite-Dimensional Discrete Systems Integrated in Quadratures

T. G. Kazakova

Sterlitamak State Pedagogical Institute

Abstract: We consider finite-dimensional reductions (truncations) of discrete systems of the type of the Toda chain with discrete time that retain the integrability. We show that for finite-dimensional chains, in addition to integrals of motion, we can construct a rich family of higher symmetries described by the master symmetry. We reduce the problem of integrating a finite-dimensional system to the implicit function theorem.

Keywords: integrability, truncation condition, zero-curvature equation, classical symmetry, master symmetry, integrals of motion

DOI: https://doi.org/10.4213/tmf30

Full text: PDF file (258 kB)
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English version:
Theoretical and Mathematical Physics, 2004, 138:3, 356–369

Bibliographic databases:

Received: 04.04.2003

Citation: T. G. Kazakova, “Finite-Dimensional Discrete Systems Integrated in Quadratures”, TMF, 138:3 (2004), 422–436; Theoret. and Math. Phys., 138:3 (2004), 356–369

Citation in format AMSBIB
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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. Kazakova, TG, “Finite-dimensional reductions of the discrete Toda chain”, Journal of Physics A-Mathematical and General, 37:33 (2004), 8089  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    2. Gudkova EV, “Finite reductions of the two dimensional Toda chain”, Journal of Nonlinear Mathematical Physics, 12 (2005), 197–205, Suppl. 2  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    3. I. T. Habibullin, “C-Series Discrete Chains”, Theoret. and Math. Phys., 146:2 (2006), 170–182  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    4. V. L. Vereshchagin, “Soliton solutions of an integrable boundary problem on the half-line for the discrete Toda chain”, Theoret. and Math. Phys., 148:3 (2006), 1199–1209  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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