Overview
- Offers a comprehensive introduction to the field of symmetries and integrability of difference equations from nine different perspectives
- Presents many examples and exercises to make it easily accessible to researchers new to the field
- Contains up-to-date bibliographies in each chapter for researchers interested in studying the field in greater depth
- Includes supplementary material: sn.pub/extras
Part of the book series: CRM Series in Mathematical Physics (CRM)
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About this book
This book shows how Lie group and integrability techniques, originally developed for differential equations, have been adapted to the case of difference equations. Difference equations are playing an increasingly important role in the natural sciences. Indeed, many phenomena are inherently discrete and thus naturally described by difference equations.
More fundamentally, in subatomic physics, space-time may actually be discrete. Differential equations would then just be approximations of more basic discrete ones. Moreover, when using differential equations to analyze continuous processes, it is often necessary to resort to numerical methods. This always involves a discretization of the differential equations involved, thus replacing them by difference ones.
Each of the nine peer-reviewed chapters in this volume serves as a self-contained treatment of a topic, containing introductory material as well as the latest research results and exercises. Each chapter is presented by one or more early career researchers in the specific field of their expertise and, in turn, written for early career researchers. As a survey of the current state of the art, this book will serve as a valuable reference and is particularly well suited as an introduction to the field of symmetries and integrability of difference equations. Therefore, the book will be welcomed by advanced undergraduate and graduate students as well as by more advanced researchers.Similar content being viewed by others
Keywords
Table of contents (9 chapters)
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Front Matter
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Back Matter
Editors and Affiliations
Bibliographic Information
Book Title: Symmetries and Integrability of Difference Equations
Book Subtitle: Lecture Notes of the Abecederian School of SIDE 12, Montreal 2016
Editors: Decio Levi, Raphaël Rebelo, Pavel Winternitz
Series Title: CRM Series in Mathematical Physics
DOI: https://doi.org/10.1007/978-3-319-56666-5
Publisher: Springer Cham
eBook Packages: Physics and Astronomy, Physics and Astronomy (R0)
Copyright Information: Springer International Publishing AG 2017
Hardcover ISBN: 978-3-319-56665-8Published: 11 July 2017
Softcover ISBN: 978-3-319-85967-5Published: 02 August 2018
eBook ISBN: 978-3-319-56666-5Published: 30 June 2017
Series ISSN: 2627-7654
Series E-ISSN: 2627-7662
Edition Number: 1
Number of Pages: X, 435
Number of Illustrations: 41 b/w illustrations, 26 illustrations in colour
Topics: Numerical and Computational Physics, Simulation, Difference and Functional Equations, Field Theory and Polynomials