Discrete Systems and Integrability

ISBN-13: 9781107042728 / Angielski / Twarda / 2016 / 458 str.

Jarmo Hietarinta; Nalini Joshi; Frank Nijhoff

Opis

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

Spis treści

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.