Symmetries and Integrability of Difference Equations

Symmetries and Integrability of Difference Equations

by Decio Levi
     
 

ISBN-10: 052113658X

ISBN-13: 9780521136587

Pub. Date: 06/30/2011

Publisher: Cambridge University Press

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

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Overview

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.

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Product Details

ISBN-13:
9780521136587
Publisher:
Cambridge University Press
Publication date:
06/30/2011
Series:
London Mathematical Society Lecture Note Series, #381
Pages:
360
Product dimensions:
5.90(w) x 8.90(h) x 0.70(d)

Table of Contents

1. Lagrangian and Hamiltonian formalism for discrete equations: symmetries and first integrals V. Dorodnitsyn 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.

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