Symmetries and integrability of difference equations / edited by Decio Levi [and others].

Format:

Book

Contributor:

Levi, D. (Decio), editor.

Series:

London Mathematical Society lecture note series ; 381.

London Mathematical Society lecture note series ; 381

Language:

English

Subjects (All):

Difference equations.

Symmetry (Mathematics).

Integrals.

Physical Description:

1 online resource (xviii, 341 pages) : digital, PDF file(s).

Other Title:

Symmetries & Integrability of Difference Equations

Place of Publication:

Cambridge : Cambridge University Press, 2011.

Language Note:

English

Summary:

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.

Contents:

Lagrangian and Hamiltonian formalism for discrete equations: symmetries and first integrals / V. Dorodnitsyn and R. Kozlov

Painlevé equations: continuous, discrete and ultradiscrete / B. Grammaticos and A. Ramani

Definitions and predictions of integrability for difference equations / J. Hietarinta

Orthogonal polynomials, their recursions, and functional equations / M.E.H. Ismail

Discrete Painlevé equations and orthogonal polynomials / A. Its

Generalized Lie symmetries for difference equations / D. Levi and R.I. Yamilov

Four lectures on discrete systems / S.P. Novikov

Lectures on moving frames / P.J. Olver

Lattices of compact semisimple Lie groups / J. Patera

Lectures on discrete differential geometry / Yu. B Suris

Symmetry preserving discretization of differential equations and Lie point symmetries of differential-difference equations / P. Winternitz.

Notes:

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Includes bibliographical references.

ISBN:

1-107-21324-X

1-280-77609-9

1-139-12283-5

9786613686480

1-139-11709-2

1-139-12775-6

1-139-11273-2

0-511-99713-2

1-139-11492-1

OCLC:

769341701