Discrete integrable systems [... contains ten courses based on the lectures delivered at the International School on Discrete Integrable Systems, ... which was held in Pondicherry, India, from February 2 to February 14, 2003

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. The Lectures That Comprise This Volume Constitute A Comprehensive Survey Of The Many And Various Aspects Of Integrable Dynamical Systems. The Present Edition Is A Streamlined, Revised And Updated Version Of A 1997 Set Of Notes That Was Published As Lecture Notes In Physics, Volume 495. This Volume Will Be Complemented By A Companion Book Dedicated To Discrete Integrable Systems. 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. Nonlinear Waves, Solitons, And Ist (m.j. Ablowitz) -- Integrability - - And How To Detect It (b. Grammaticos, A. Ramani) -- Introduction To The Hirota Bilinear Method (j. Hietarinta) -- Lie Bialgebras, Poisson Lie Groups, And Dressing Transformations (y. Kosmann-schwarzbach) -- Analytic And Asymptotic Methods For Nonlinear Singularity Analysis: A Review And Extensions Of Tests For The Painlevé Property (m.d. Kruskal, N. Joshi, R. Halburd) -- Eight Lectures On Integrable Systems (f. Magri, P. Casati, G. Falqui, M. Pedroni) -- Bilinear Formalism In Soliton Theory (j. Satsuma) -- Quantum And Classical Integrable Systems ( M.a. Semenov-tian-shansky). Y. Kosmann-schwarzbach, B. Grammaticos, K.m. Tamizhmani (eds.). Includes Bibliographical References. 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. TOC:Three Lessons on the Painlevé Property and the Painlevé Equations.- Sato Theory and Transformation Groups.- A Unified Approach to Integrable Systems.- Special Solutions of Discrete Integrable Systems.- Discrete Differential Geometry. Integrability as Consistency.- Discrete Lagrangian Models.- Symmetries of Discrete Systems.- Discrete Painlevé Equations: a Review.- Special Solutions for Discrete Painlevé Equations.- Ultradiscrete Systems (Cellular Automata).- Time in Science: Reversibility vs. Irreversibility Three lessons on the Painlevé property and the Painlevé equations / M.D. Kruskal, B. Grammaticos, T. Tamizhmani Sato theory and transformation groups: a unified approach to integrable systems / R. Willox, J. Satsuma Special solutions of discrete integrable systems / Y. Ohta Discrete differential geometry : integrability as consistency / A.I. Bobenko Discrete Lagrangian models / Yu. B. Suris Symmetries of discrete systems / P. Winternitz Discrete Painlevé equations : a review / B. Grammaticos, A. Ramani Special solutions for discrete Painlevé equations / K.M. Tamizhmani ... [et al.] Ultradiscrete systems (cellular automata) / T. Tokihiro Time in science : reversibility vs. irreversibility / Y. Pomeau. 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 "This volume consists of a set of ten lectures conceived as both introduction and up-to-date survey on discrete integrable systems. It address primarily graduate students and nonspecialist researchers but will also benefit lectures looking for suitable material for advanced courses and researchers interested in specific topics."--Jacket