Symmetries and Integrability of Difference Equations Lecture Notes of the Abecederian School of SIDE 12, Montreal 2016 /

• Corporate Author: SpringerLink (Online service)
• Other Authors: Levi, Decio (Editor), Rebelo, Raphaël (Editor), Winternitz, Pavel (Editor)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2017.
• Series: CRM Series in Mathematical Physics
• Subjects: Physics.; Algebra.; Field theory (Physics).; Difference equations.; Functional equations.; Numerical and Computational Physics, Simulation.; Difference and Functional Equations.; Field Theory and Polynomials.

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...

Table of 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.