Symmetries and integrability of difference equations
- Cambridge ; New York : Cambridge University Press, 2011.
- Physical description
- xviii, 341 p. : ill. ; 23 cm.
- London Mathematical Society lecture note series ; 381.
QA431 .S952 2008
- Unknown QA431 .S952 2008
- Includes bibliographical references.
- 1. Lagrangian and Hamiltonian formalism for discrete equations: symmetries and first integrals V. Dorodnitsyn and R. Kozlov-- 2. Painleve equations: continuous, discrete and ultradiscrete B. Grammaticos and A. Ramani-- 3. Definitions and predictions of integrability for difference equations J. Hietarinta-- 4. Orthogonal polynomials, their recursions, and functional equations M. E. H. Ismail-- 5. Discrete Painleve equations and orthogonal polynomials A. Its-- 6. Generalized Lie symmetries for difference equations D. Levi and R. I. Yamilov-- 7. Four lectures on discrete systems S. P. Novikov-- 8. Lectures on moving frames P. J. Olver-- 9. Lattices of compact semisimple Lie groups J. Patera-- 10. Lectures on discrete differential geometry Yu. B Suris-- 11. Symmetry preserving discretization of differential equations and Lie point symmetries of differential-difference equations P. Winternitz.
- (source: Nielsen Book Data)
- Publisher's Summary
- Difference equations are playing an increasingly important role in the natural sciences. Indeed many phenomena are inherently discrete and are naturally described by difference equations. Phenomena described by differential equations are therefore approximations of more basic discrete ones. Moreover, in their study it is very often necessary to resort to numerical methods. This always involves a discretization of the differential equations involved, thus replacing them by difference equations. This book shows how Lie group and integrability techniques, originally developed for differential equations, have been adapted to the case of difference ones. Each of the eleven chapters is a self-contained treatment of a topic, containing introductory material as well as the latest research results. The book will be welcomed by graduate students and researchers seeking an introduction to the field. As a survey of the current state of the art it will also serve as a valuable reference.
(source: Nielsen Book Data)
- Publication date
- edited by Decio Levi ... [et al.].
- London Mathematical Society lecture note series ; 381
- Published in association with the London Mathematical Society.
- "... based upon lectures delivered during the Summer School on Symmetries and Integrability of Difference Equations at the Université de Montréal, Canada, June 8, 2008-June 21, 2008"--Pref.