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Symmetries and integrability of difference equations = lecture notes of the Abecederian School of SIDE 12, Montreal 2016 /

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Symmetries and integrability of difference equations/ edited by Decio Levi, Raphael Rebelo, Pavel Winternitz.
Reminder of title:	lecture notes of the Abecederian School of SIDE 12, Montreal 2016 /
other author:	Levi, Decio.
corporate name:	Workshop on the Preservation of Stability under Discretization
Published:	Cham :Springer International Publishing : : 2017.,
Description:	x, 435 p. :ill., digital ; : 24 cm.;
Contained By:	Springer eBooks
Subject:	Differential equations - Textbooks. -
Online resource:	http://dx.doi.org/10.1007/978-3-319-56666-5
ISBN:	9783319566665

Symmetries and integrability of difference equations = lecture notes of the Abecederian School of SIDE 12, Montreal 2016 /
Symmetries and integrability of difference equationslecture notes of the Abecederian School of SIDE 12, Montreal 2016 /[electronic resource] :edited by Decio Levi, Raphael Rebelo, Pavel Winternitz. - Cham :Springer International Publishing :2017. - x, 435 p. :ill., digital ;24 cm. - CRM series in mathematical physics. - CRM series in mathematical physics..

Chapter 1. Continuous, Discrete and Ultradiscrete Painleve 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.

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.

ISBN: 9783319566665

Standard No.: 10.1007/978-3-319-56666-5doiSubjects--Topical Terms:

1027753
Differential equations
--Textbooks.

LC Class. No.: QA370

Dewey Class. No.: 515.35

Symmetries and integrability of difference equations = lecture notes of the Abecederian School of SIDE 12, Montreal 2016 /
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505 0 $a Chapter 1. Continuous, Discrete and Ultradiscrete Painleve 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.
520 $a 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.
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