Discrete Integrable Systems

M.D. Kruskal, B. Grammaticos, T. Tamizhmani (auth.), Basil Grammaticos, Thamizharasi Tamizhmani, Yvette Kosmann-Schwarzbach (eds.)3540214259, 9783540214250

This volume consists of a set of ten lectures conceived as both introduction and up-to-date survey on discrete integrable systems. It constitutes a companion book to “Integrability of Nonlinear Systems” (Springer-Verlag, 2004, LNP 638, ISBN 3-540-20630-2). Both volumes address primarily graduate students and nonspecialist researchers but will also benefit lecturers looking for suitable material for advanced courses and researchers interested in specific topics.

Table of contents :
Three Lessons on the Painlevé Property and the Painlevé Equations….Pages 1-15
Sato Theory and Transformation Groups. A Unified Approach to Integrable Systems….Pages 17-55
Special Solutions of Discrete Integrable Systems….Pages 57-83
Discrete Differential Geometry. Integrability as Consistency….Pages 85-110
Discrete Lagrangian Models….Pages 111-184
Symmetries of Discrete Systems….Pages 185-243
Discrete Painlevé Equations: A Review….Pages 245-321
Special Solutions for Discrete Painlevé Equations….Pages 323-382
Ultradiscrete Systems (Cellular Automata)….Pages 383-424
Time in Science: Reversibility vs. Irreversibility….Pages 425-436