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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Format: | eBook |
Language: | English |
Published: |
Basel
Birkhäuser Basel
2003, 2003
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Edition: | 1st ed. 2003 |
Series: | Progress in Mathematics
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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