J. Hietarinta

Discrete Systems and Integrability (eBook, ePUB)

• Format: ePub

Produktbeschreibung

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 Backlund transformations; difference equations and special functions; multidimensional consistency of integrable lattice equations; associated linear problems (Lax pairs); connections with Pade approximants and convergence algorithms; singularities and geometry; Hirota's bilinear formalism for lattices; intriguing properties of discrete Painleve 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.

---

Dieser Download kann aus rechtlichen Gründen nur mit Rechnungsadresse in A, B, BG, CY, CZ, D, DK, EW, E, FIN, F, GR, HR, H, IRL, I, LT, L, LR, M, NL, PL, P, R, S, SLO, SK ausgeliefert werden.

Produktdetails

• Verlag: Cambridge University Press
• Erscheinungstermin: 19. August 2016
• Englisch
• ISBN-13: 9781316653036
• Artikelnr.: 53002398

Autorenporträt

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).

Inhaltsangabe

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.