Look Inside Symmetries and Integrability of Difference Equations

Symmetries and Integrability of Difference Equations

Part of London Mathematical Society Lecture Note Series

Editors:
Decio Levi, Università degli Studi Roma Tre
Peter Olver, University of Minnesota
Zora Thomova, SUNY Institute of Technology
Pavel Winternitz, Université de Montréal

V. Dorodnitsyn, R. Kozlov, B. Grammaticos, A. Ramani, J. Hietarinta, M. E. H. Ismail, A. Its, D. Levi, R. I. Yamilov, S. P. Novikov, P. J. Olver, J. Patera, Yu. B. Suris, P. Winternitz

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Date Published: June 2011
availability: Available
format: Paperback
isbn: 9780521136587

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Description

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.
- Shows how Lie group and integrability techniques, originally developed for differential equations, have been adapted for difference equations
- Each chapter covers a single topic, and includes introductory material as well as the latest research results
- An ideal introduction to the subject for students and researchers
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Reviews & endorsements
'The book can certainly be recommended to everyone interested in having a comprehensive overview of the current state of the art in this fascinating and important research field.' Frans Cantrijn, Mathematical Reviews

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Product details
- Date Published: June 2011
- format: Paperback
- isbn: 9780521136587
- length: 360 pages
- dimensions: 228 x 151 x 18 mm
- weight: 0.51kg
- contains: 40 b/w illus.
- availability: Available
Table of Contents
1. Lagrangian and Hamiltonian formalism for discrete equations: symmetries and first integrals V. Dorodnitsyn and R. Kozlov
2. Painlevé 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 Painlevé 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.
Look Inside
Editors
Decio Levi, Università degli Studi Roma Tre
Decio Levi is a researcher in the Faculty of Engineering at the Università degli Studi Roma Tre.
Peter Olver, University of Minnesota
Peter Olver is a Professor and currently Head of the School of Mathematics at the University of Minnesota.
Zora Thomova, SUNY Institute of Technology
Zora Thomova is an Associate Professor of Mathematics at the State University of New York – Institute of Technology.
Pavel Winternitz, Université de Montréal
Pavel Winternitz is a Professor in the Department of Mathematics and Statistics at the Université de Montréal.
Contributors
V. Dorodnitsyn, R. Kozlov, B. Grammaticos, A. Ramani, J. Hietarinta, M. E. H. Ismail, A. Its, D. Levi, R. I. Yamilov, S. P. Novikov, P. J. Olver, J. Patera, Yu. B. Suris, P. Winternitz