Discrete Systems and Integrability - F W Nijhoff

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Résumé :
A first introduction to the theory of discrete integrable systems at a level suitable for students and non-experts.

Biographie:
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).

Sommaire:
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 Painlev? equations; 12. Lagrangian multiform theory; Appendix A. Elementary difference calculus and difference equations; Appendix B. Theta functions and elliptic functions; Appendix C. The continuous Painlev? equations and the Garnier system; Appendix D. Some determinantal identities; References; Index.