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Author:   J. Hietarinta (University of Turku, Finland) ,  N. Joshi (University of Sydney) ,  F. W. Nijhoff (University of Leeds)
Publisher:   Cambridge University Press
Imprint:   Cambridge University Press
Volume:   54
Dimensions:   Width: 17.30cm , Height: 2.50cm , Length: 24.60cm
Weight:   0.820kg
ISBN:  

9781107669482

ISBN 10:   1107669480
Pages:   458
Publication Date:   19 August 2016
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   Available To Order  
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Table of Contents

Preface; 1. Introduction to difference equations; 2. Discrete equations from transformations of continuous equations; 3. Integrability of P∆Es; 4. Interlude: lattice equations and numerical algorithms; 5. Continuum limits of lattice P∆Es; 6. One-dimensional lattices and maps; 7. Identifying integrable difference equations; 8. Hirota's bilinear method; 9. Multi-soliton solutions and the Cauchy matrix scheme; 10. Similarity reductions of integrable P∆Es; 11. Discrete Painlevé equations; 12. Lagrangian multiform theory; Appendix A. Elementary difference calculus and difference equations; Appendix B. Theta functions and elliptic functions; Appendix C. The continuous Painlevé equations and the Garnier system; Appendix D. Some determinantal identities; References; Index.

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Author Information

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). N. Joshi is Professor of Applied Mathematics at the University of Sydney. She is best known for her work on the Painlevé equations and works at the leading edge of international efforts to analyse discrete and continuous integrable systems in the geometric setting of their initial-value spaces, constructed by resolving singularities in complex projective space. She was elected as a Fellow of the Australian Academy of Science in 2008, holds a Georgina Sweet Australian Laureate Fellowship and was awarded the special Hardy Fellowship of the London Mathematical Society in 2015. F. W. Nijhoff is Professor of Mathematical Physics in the School of Mathematics at the University of Leeds. His research focuses on nonlinear difference and differential equations, symmetries and integrability of discrete systems, variational calculus, quantum integrable systems and linear and nonlinear special functions. He was the principal organizer of the 2009 six-month programme on Discrete Integrable Systems at the Isaac Newton Institute, and was awarded a Royal Society Leverhulme Trust Senior Research Fellow in 2011.

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