Symmetries and Integrability of Difference Equations [electronic resource] Lecture Notes of the Abecederian School of SIDE 12, Montreal 2016 / edited by Decio Levi, Raphaël Rebelo, Pavel Winternitz.

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...

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Bibliographic Details
Uniform Title:CRM Series in Mathematical Physics, 2627-7662
Corporate Author: SpringerLink (Online service)
Other Authors: Levi, Decio (Editor)
Rebelo, Raphaël (Editor)
Winternitz, Pavel (Editor)
Language:English
Published: Cham : Springer International Publishing : Imprint: Springer, 2017.
Edition:1st ed. 2017.
Series:CRM Series in Mathematical Physics,
Subjects:
Mathematical physics.
Difference equations.
Functional equations.
Algebraic fields.
Polynomials.
Online Access:
Springer Physics and Astronomy eBooks 2017 English/International: 2017 (Springer Link)
Format: Electronic eBook
Contents:
  • Chapter 1. Continuous, Discrete and Ultradiscrete Painlevé Equations
  • Chapter 2. Elliptic Hypergeometric Functions
  • Chapter 3. Integrability of Difference Equations through Algebraic Entropy and Generalized Symmetries
  • Chapter 4. Introduction to Linear and Nonlinear Integrable Theories in Discrete Complex Analysis
  • Chapter 5. Discrete Integrable Systems, Darboux Transformations and Yang–Baxter Maps
  • Chapter 6. Symmetry-Preserving Numerical Schemes
  • Chapter 7. Introduction to Cluster Algebras
  • Chapter 8. An Introduction to Difference Galois Theory
  • Chapter 9. Lectures on Quantum Integrability: Lattices, Symmetries and Physics.