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Discrete systems and integrability

Hietarinta, J.

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Discrete systems and integrability

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Discrete systems and integrability/ J. Hietarinta, N. Joshi, F.W. Nijhoff.
作者:	Hietarinta, J.
其他作者:	Joshi, Nalini.
出版者:	Cambridge :Cambridge University Press, : 2016.,
面頁冊數:	xiii, 445 p. :digital ;24 cm.
附註:	Title from publisher's bibliographic system (viewed on 06 Sep 2016).
內容註:	Introduction to difference equations -- Discrete equations from transformations of continuous equations -- Integrability of PEs -- Interlude: lattice equations and numerical algorithms -- Continuum limits of lattice PE -- One-dimensional lattices and maps -- Identifying integrable difference equations -- Hirota's bilinear method -- Multi-soliton solutions and the Cauchy matrix scheme -- Similarity reductions of integrable PE's -- Discrete Painleve equations -- Lagrangian multiform theory.
標題:	Integral equations. -
電子資源:	https://doi.org/10.1017/CBO9781107337411
ISBN:	9781107337411

Discrete systems and integrability
Hietarinta, J.

Discrete systems and integrability[electronic resource] /J. Hietarinta, N. Joshi, F.W. Nijhoff. - Cambridge :Cambridge University Press,2016. - xiii, 445 p. :digital ;24 cm. - Cambridge texts in applied mathematics. - Cambridge texts in applied mathematics..

Title from publisher's bibliographic system (viewed on 06 Sep 2016).

Introduction to difference equations -- Discrete equations from transformations of continuous equations -- Integrability of PEs -- Interlude: lattice equations and numerical algorithms -- Continuum limits of lattice PE -- One-dimensional lattices and maps -- Identifying integrable difference equations -- Hirota's bilinear method -- Multi-soliton solutions and the Cauchy matrix scheme -- Similarity reductions of integrable PE's -- Discrete Painleve equations -- 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 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; singularities and geometry; 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.

ISBN: 9781107337411Subjects--Topical Terms:

589037
Integral equations.

LC Class. No.: QC20.7.I58 / H54 2016

Dewey Class. No.: 511.1

Discrete systems and integrability
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500 $a Title from publisher's bibliographic system (viewed on 06 Sep 2016).
505 0 $a Introduction to difference equations -- Discrete equations from transformations of continuous equations -- Integrability of PEs -- Interlude: lattice equations and numerical algorithms -- Continuum limits of lattice PE -- One-dimensional lattices and maps -- Identifying integrable difference equations -- Hirota's bilinear method -- Multi-soliton solutions and the Cauchy matrix scheme -- Similarity reductions of integrable PE's -- Discrete Painleve equations -- Lagrangian multiform theory.
520 $a 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; singularities and geometry; 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.
650 0 $a Integral equations. $3 589037
650 0 $a Mathematical physics. $3 516853
700 1 $a Joshi, Nalini. $3 3440308
700 1 $a Nijhoff, Frank W. $3 3440309
830 0 $a Cambridge texts in applied mathematics. $3 3440310
856 4 0 $u https://doi.org/10.1017/CBO9781107337411