Symmetries and Integrability of Difference Equations
- English
- PDF
- Available on iOS & Android
Symmetries and Integrability of Difference Equations
About this book
Difference equations are playing an increasingly important role in the natural sciences. Indeed many phenomena are inherently discrete and are naturally described by difference equations. Phenomena described by differential equations are therefore approximations of more basic discrete ones. Moreover, in their study it is very often necessary to resort to numerical methods. This always involves a discretization of the differential equations involved, thus replacing them by difference equations. This book shows how Lie group and integrability techniques, originally developed for differential equations, have been adapted to the case of difference ones. Each of the eleven chapters is a self-contained treatment of a topic, containing introductory material as well as the latest research results. The book will be welcomed by graduate students and researchers seeking an introduction to the field. As a survey of the current state of the art it will also serve as a valuable reference.
Frequently asked questions
- Essential is ideal for learners and professionals who enjoy exploring a wide range of subjects. Access the Essential Library with 800,000+ trusted titles and best-sellers across business, personal growth, and the humanities. Includes unlimited reading time and Standard Read Aloud voice.
- Complete: Perfect for advanced learners and researchers needing full, unrestricted access. Unlock 1.4M+ books across hundreds of subjects, including academic and specialized titles. The Complete Plan also includes advanced features like Premium Read Aloud and Research Assistant.
Please note we cannot support devices running on iOS 13 and Android 7 or earlier. Learn more about using the app.
Information
Table of contents
- Cover
- Title
- Copyright
- Contents
- List of figures
- List of contributors
- Preface
- Introduction
- 1 Lagrangian and Hamiltonian Formalism for Discrete Equations: Symmetries and First Integrals V. orodnitsyn and R. Kozlov
- 2 Painlevé Equations: Continuous, Discrete and Ultradiscrete B. Grammaticos and A. Ramani
- 3 Definitions and Predictions of Integrability for Difference Equations J. Hietarinta
- 4 Orthogonal Polynomials, their Recursions, and Functional Equations M. E. H. Ismail
- 5 Discrete Painlevé Equations and Orthogonal Polynomials A. Its
- 6 Generalized Lie Symmetries for Difference Equations D. Levi and R. I. Yamilov
- 7 Four Lectures on Discrete Systems S. P. Novikov
- 8 Lectures on Moving Frames P. J. Olver
- 9 Lattices of Compact Semisimple Lie Groups J. Patera
- 10 Lectures on Discrete Differential Geometry Yu. B Suris
- 11 Symmetry Preserving Discretization of Differential Equations and Lie Point Symmetries of Differential-Difference Equations P. Winternitz