Symmetries and Integrability of Difference Equations

Lecture Notes of the Abecederian School of SIDE 12, Montreal 2016

  • Decio Levi
  • Raphaël Rebelo
  • Pavel Winternitz

Part of the CRM Series in Mathematical Physics book series (CRM)

Table of contents

  1. Front Matter
    Pages i-x
  2. Nobutaka Nakazono, Yang Shi, Masataka Kanki
    Pages 1-41
  3. Fokko J. van de Bult
    Pages 43-74
  4. Deniz Bilman, Sotiris Konstantinou-Rizos
    Pages 195-260
  5. Alexander Bihlo, Francis Valiquette
    Pages 261-324
  6. Max Glick, Dylan Rupel
    Pages 325-357
  7. Julien Roques
    Pages 359-390
  8. Back Matter
    Pages 431-435

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.


discrete Painlevé equations Orthogonal polynomials Discrete integrable systems Yang-Baxter maps Difference Galois theory multivariable difference equations differential difference equations

Editors and affiliations

  • Decio Levi
    • 1
  • Raphaël Rebelo
    • 2
  • Pavel Winternitz
    • 3
  1. 1.Mathematics and Physics Departments, and INFN, Sezione Roma TreRoma Tre UniversityRomaItaly
  2. 2.Collège AhuntsicMontréalCanada
  3. 3.Centre de Recherches Mathématiques and Département de Mathématiques et de StatistiqueUniversité de MontréalMontréalCanada

Bibliographic information

  • DOI
  • Copyright Information Springer International Publishing AG 2017
  • Publisher Name Springer, Cham
  • eBook Packages Physics and Astronomy
  • Print ISBN 978-3-319-56665-8
  • Online ISBN 978-3-319-56666-5
  • Buy this book on publisher's site