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Teoreticheskaya i Matematicheskaya Fizika, 2004, Volume 138, Number 3, Pages 422–436
DOI: https://doi.org/10.4213/tmf30 (Mi tmf30) 		 
This article is cited in 5 scientific papers (total in 5 papers)

Finite-Dimensional Discrete Systems Integrated in Quadratures

T. G. Kazakova

Sterlitamak State Pedagogical Institute
Full-text PDF (258 kB) Citations (5)
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DOI: https://doi.org/10.4213/tmf30
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.
Received: 04.04.2003
English version:
Theoretical and Mathematical Physics, 2004, Volume 138, Issue 3, Pages 356–369
DOI: https://doi.org/10.1023/B:TAMP.0000018452.62337.c8
Bibliographic databases:
Language: Russian
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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  • https://www.mathnet.ru/eng/tmf30
  • https://doi.org/10.4213/tmf30
  • https://www.mathnet.ru/eng/tmf/v138/i3/p422
    • This publication is cited in the following 5 articles:
    1. T. G. Kazakova, R. R. Sattarova, “Novyi primer konechnomernoi reduktsii diskretnoi tsepochki tipa tsepochki Tody”, Izvestiya vysshikh uchebnykh zavedenii. Povolzhskii region. Fiziko-matematicheskie nauki, 2020, no. 3, 85–97  mathnet  crossref
    2. I. T. Habibullin, “C-Series Discrete Chains”, Theoret. and Math. Phys., 146:2 (2006), 170–182  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    3. 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
    4. 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
    5. 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
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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    Full-text PDF :231
    References:81
    First page:1
     
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