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Fundamental Models on the Lattice

  • Ludwig D. Faddeev
  • Leon A. Takhtajan
Part of the Springer Series in Soviet Mathematics book series (CLASSICS)

Abstract

Here we shall give a complete list of results pertaining to the Toda model, a fundamental model on the lattice. We will show that the r-matrix approach applies to this case and may be used to prove the complete integrability of the model in the quasi-periodic case. For the rapidly decreasing boundary conditions we will analyze the mapping F from the initial data of the auxiliary linear problem to the transition coefficients and outline a method for solving the inverse problem, i.e. for F−1 constructing. On the basis of the r-matrix approach it will be shown that F is a canonical trans formation to action-angle type variables establishing the complete integrability of the Toda model in the rapidly decreasing case. We shall also define a lattice version of the LL model, the most general integrable lattice system with two-dimensional auxiliary space.

Keywords

Integral Equation Inverse Problem Global Analysis Linear Problem Type Variable 
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

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Ludwig D. Faddeev
    • 1
  • Leon A. Takhtajan
    • 1
  1. 1.Steklov Mathematical InstituteLeningradUSSR

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