Online Public Access Catalogue (OPAC)
Library,Documentation and Information Science Division

“A research journal serves that narrow

borderland which separates the known from the unknown”

-P.C.Mahalanobis


Image from Google Jackets

Discrete systems and integrability / J. Hietarinta, N. Joshi and F.W. Nijhoff.

By: Contributor(s): Material type: TextTextSeries: Cambridge texts in applied mathematicsPublication details: Cambridge : Cambridge University Press, 2016.Description: xiii, 445 pages : illustrations ; 25 cmISBN:
  • 9781107669482 (paperback)
Subject(s): DDC classification:
  • 511.1 23 H633
Contents:
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∆E -- 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.
Summary: "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 Bäcklund transformations, difference equations and special functions, multidimensional consistency of integrable lattice equations, associated linear problems (Lax pairs), connections with Padé approximants and convergence algorithms, Hirota's bilinear formalism for lattices, intriguing properties of discrete Painlevé 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"--
Tags from this library: No tags from this library for this title. Log in to add tags.

Includes bibliographical references and index.

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∆E --
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.

"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 Bäcklund transformations, difference equations and special functions, multidimensional consistency of integrable lattice equations, associated linear problems (Lax pairs), connections with Padé approximants and convergence algorithms, Hirota's bilinear formalism for lattices, intriguing properties of discrete Painlevé 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"--

There are no comments on this title.

to post a comment.
Library, Documentation and Information Science Division, Indian Statistical Institute, 203 B T Road, Kolkata 700108, INDIA
Phone no. 91-33-2575 2100, Fax no. 91-33-2578 1412, ksatpathy@isical.ac.in