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Theoretical and Mathematical Physics

, Volume 118, Issue 2, pp 173–182 | Cite as

Integrable lattices

  • V. G. Marikhin
  • A. B. Shabat
Article

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.

Keywords

Discrete Equation Heisenberg Model Toda Lattice Integrable Lattice Toda Chain 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Kluwer Academic/Plenum Publishers 1999

Authors and Affiliations

  • V. G. Marikhin
    • 1
  • A. B. Shabat
    • 1
  1. 1.Landau Institute for Theoretical PhysicsRussian Academy of SciencesMoscowRussia

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