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Teoreticheskaya i Matematicheskaya Fizika, 1999, Volume 118, Number 2, Pages 217–228
DOI: https://doi.org/10.4213/tmf695 (Mi tmf695) 		 
This article is cited in 15 scientific papers (total in 15 papers)

Integrable lattices

V. G. Marikhin, A. B. Shabat

L. D. Landau Institute for Theoretical Physics, Russian Academy of Sciences
Full-text PDF (212 kB) Citations (15)
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DOI: https://doi.org/10.4213/tmf695
Abstract: We propose a method for constructing integrable lattices starting from dynamic systems with two different parameterizations of the canonical variables and hence two independent Bäcklund flows. We construct integrable lattices corresponding to generalizations of the nonlinear Schrödinger equation. We discuss the Toda, Volterra, and Heisenberg models in detail. For these systems, as well as for the Landau–Lifshitz model, we obtain totally discrete Lagrangians. We also discuss the relation of these systems to the Hirota equations.
Received: 21.07.1997
English version:
Theoretical and Mathematical Physics, 1999, Volume 118, Issue 2, Pages 173–182
DOI: https://doi.org/10.1007/BF02557310
Bibliographic databases:
Language: Russian
Citation: V. G. Marikhin, A. B. Shabat, “Integrable lattices”, TMF, 118:2 (1999), 217–228; Theoret. and Math. Phys., 118:2 (1999), 173–182
Citation in format AMSBIB
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    • This publication is cited in the following 15 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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    References:99
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