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Discrete systems and integrability

By: Hietarinta, J.
Contributor(s): Joshi, Nalini | Nijhoff, Frank W.
Material type: materialTypeLabelBookSeries: Publisher: Cambridge Cambridge University Press 2016Description: xiii, 445 p.ISBN: 9781107669482.Subject(s): Integral Equations | Mathematical Physics | Darboux and Backlund TransformationsDDC classification: 511.1 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 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." https://www.goodreads.com/book/show/30462584-discrete-systems-and-integrability?from_search=true
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Books Vikram Sarabhai Library
Slot 1352 (0 Floor, East Wing) Non-fiction 511.1 H4D4 (Browse shelf) Available 193747

1 Introduction to difference equations
2 Discrete equations from transformations of continuous equations
3 Integrability of PEs
4 Interlude: lattice equations and numerical algorithms
5 Continuum limits of lattice PE
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 PE's
11 Discrete Painlevé equations
12 Lagrangian multiform theory

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."

https://www.goodreads.com/book/show/30462584-discrete-systems-and-integrability?from_search=true

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