Discrete Systems and Integrability (Cambridge Texts in Applied Mathematics, Series Number 54) - Softcover

Hietarinta, J.; Joshi, N.; Nijhoff, F. W.

Softcover

ISBN 10: 1107669480 ISBN 13: 9781107669482

Publisher: Cambridge University Press, 2016

Synopsis

This first introductory text to discrete integrable systems introduces key notions of integrability from the vantage point of discrete systems, also making connections with the continuous theory where relevant. While treating the material at an elementary level, the book also highlights many recent developments. Topics include: Darboux and Bäcklund transformations; difference equations and special functions; multidimensional consistency of integrable lattice equations; associated linear problems (Lax pairs); connections with Padé approximants and convergence algorithms; singularities and geometry; Hirota's bilinear formalism for lattices; intriguing properties of discrete Painlevé equations; and the novel theory of Lagrangian multiforms. The book builds the material in an organic way, emphasizing interconnections between the various approaches, while the exposition is mostly done through explicit computations on key examples. Written by respected experts in the field, the numerous exercises and the thorough list of references will benefit upper-level undergraduate, and beginning graduate students as well as researchers from other disciplines.

About this title

Book Description

The first introductory text on a topic of interdisciplinary science that has undergone major development in recent years. Written by respected experts in the field and including numerous exercises and notes on further reading, this book will benefit upper-level and beginning graduate students as well as researchers from other disciplines.

About the Author

J. Hietarinta is Professor Emeritus of Theoretical Physics at the University of Turku, Finland. His work has focused on the search for integrable systems of various forms, including Hamiltonian mechanics, Hirota bilinear form, Yang-Baxter and tetrahedron equations, as well as lattice equations. He was instrumental in the setting up of the nlin.SI category in arxiv.org and created the web pages for the SIDE (Symmetries and Integrability of Difference Equations) conference series (http://side-conference.net).

Edition details

• Publisher: Cambridge University Press
• Publication date: 2016
• ISBN 10: 1107669480
• ISBN 13: 9781107669482
• Binding: Paperback
• Language: English
• Edition number: 1
• Number of pages: 458