Cambridge University Press Symmetries and Integrability of Difference Equations: 381 (London Mathematical Society Lecture Note Series, Series Number 381)

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. Review 'The book can certainly be recommended to everyone interested in having a comprehensive overview of the current state of the art in this fascinating and important research field.' Frans Cantrijn, Mathematical Reviews Book Description A comprehensive introduction to and survey of the state of the art, suitable for graduate students and researchers alike. About the Author Decio Levi is a researcher in the Faculty of Engineering at the Università degli Studi Roma Tre.Peter Olver is a Professor and currently Head of the School of Mathematics at the University of Minnesota.Zora Thomova is an Associate Professor of Mathematics at the State University of New York – Institute of Technology.Pavel Winternitz is a Professor in the Department of Mathematics and Statistics at the Université de Montréal.