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Discrete systems and integrability /

紀錄類型:	書目-語言資料,印刷品 : 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:	Nijhoff, Frank W.,
面頁冊數:	1 online resource (xiii, 445 pages) :digital, PDF file(s). :
附註:	Title from publisher's bibliographic system (viewed on 06 Sep 2016).
標題:	Mathematical physics. -
電子資源:	https://doi.org/10.1017/CBO9781107337411
ISBN:	9781107337411 (ebook)

Discrete systems and integrability /
Hietarinta, J.

Discrete systems and integrability /J. Hietarinta, N. Joshi, F.W. Nijhoff. - 1 online resource (xiii, 445 pages) :digital, PDF file(s). - 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 Painlevé 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: 9781107337411 (ebook)Subjects--Topical Terms:

527831
Mathematical physics.

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

Dewey Class. No.: 511/.1

Discrete systems and integrability /
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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 Painlevé 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.
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650 0 $a Integral equations. $3 527971
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