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Informationen zum Autor 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). Klappentext A first introduction to the theory of discrete integrable systems at a level suitable for students and non-experts. Zusammenfassung 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. Inhaltsverzeichnis 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.
