The Problem of Integrable Discretization: Hamiltonian Approach / by Yuri B. Suris.
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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| Online Access: |
Full Text (via Springer) |
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| Main Author: | |
| Format: | eBook |
| Language: | English |
| Published: |
Basel :
Birkhäuser Basel,
2003.
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| Series: | Progress in mathematics (Boston, Mass.) ;
v. 219. |
| Subjects: |
Table of Contents:
- I. General Theory: Hamiltonian Mechanics; R-matrix Hierarchies
- II. Lattice Systems: Toda Lattice; Volterra Lattice; Newtonian Equations of the Toda Type; Relativistic Toda Lattice; Relativistic Volterra Lattice; Newtonian Equations of the Relativistic Toda Type; Explicit Discretizations for Toda Systems; Explicit Discretizations of Newtonian Toda Systems; Bruschi-Ragnisco Lattice; Multi-field Toda-like Systems; Multi-field Relativistic Toda Systems; Belov-Chaltikian Lattices; Multi-field Volterra-like Systems; Multi-field Relativistic Volterra Systems; Bogoyavlensky Lattices; Ablowitz-Ladik Hierarchy
- III. Systems of Classical Mechanics: Peakons System; Standard-like Discretizations; Lie-algebraic Toda Systems; Garnier System; Hnon-Heiles System; Neumann System; Lie-algebraic Generalizations of the Garnier Systems; Integrable Cases of Rigid Body Dynamics; Systems of Calogero-Moser Type
- Bibliography
- Notation
- Index.