The Problem of Integrable Discretization Hamiltonian Approach

The book explores the theory of discrete integrable systems, with an emphasis on the following general problem: how to discretize one or several of independent variables in a given integrable system of differential equations, maintaining the integrability property? This question (related in spirit t...

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Bibliographic Details
Main Author: Suris, Yuri B.
Format: eBook
Language:English
Published: Basel Birkhäuser Basel 2003, 2003
Edition:1st ed. 2003
Series:Progress in Mathematics
Subjects:
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
Table of Contents:
  • I General Theory
  • 1 Hamiltonian Mechanics
  • 2 R-matrix Hierarchies
  • II Lattice Systems
  • 3 Toda Lattice
  • 4 Volterra Lattice
  • 5 Newtonian Equations of the Toda Type
  • 6 Relativistic Toda Lattice
  • 7 Relativistic Volterra Lattice
  • 8 Newtonian Equations of the Relativistic Toda Type
  • 9 Explicit Discretizations for Toda Systems
  • 10 Explicit Discretizations of Newtonian Toda Systems
  • 11 Bruschi-Ragnisco Lattice
  • 12 Multi-field Toda-like Systems
  • 13 Multi-field Relativistic Toda Systems
  • 14 Belov-Chaltikian Lattices
  • 15 Multi-field Volterra-like Systems
  • 16 Multi-field Relativistic Volterra Systems
  • 17 Bogoyavlensky Lattices
  • 18 Ablowitz-Ladik Hierarchy
  • III Systems of Classical Mechanics
  • 19 Peakons System
  • 20 Standard-like Discretizations
  • 21 Lie-algebraic Toda Systems
  • 22 Gamier System
  • 23 Hénon-Heiles System
  • 24 Neumann System
  • 25 Lie-algebraic Generalizations of the Gamier Systems
  • List of Notations