Lie-Algebraic Approach to the Classification and Analysis of Integrable Models

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

Abstract

In this chapter we shall summarize and generalize our experience in describing integrable models gained from the study of particular examples. The principal entities of the inverse scattering method and its Hamiltonian interpretation were the auxiliary linear problem operator L = d/dxU(x, λ) and the fundamental Poisson brackets for U(x, λ) involving the r-matrix. Similar objects were introduced for lattice models. We will show that these notions have a simple geometric interpretation.

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© 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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