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Problem of Integrable Discretization

Name: Problem of Integrable Discretization
Brand: Birkhauser Verlag AG
SKU: 9783764369958
Price: 70439 HUF
Availability: InStock

Hamiltonian Approach

Szerző: Y. B. Suris

Nyelv:

Kötés: Kemény kötésű

Kiadó: Birkhauser Verlag AG

Elérhetőség: Beszállítói készleten

Küldés 10-13 napon belül

70 439 Ft

The book explores the theory of discrete integrable systems, with an emphasis on the following gener...

Információk a könyvről

Szerző

Y. B. Suris

Nyelv

Angol

Kötés

Könyv - Kemény kötésű

Kiadva

2003

oldal

EAN

9783764369958

ISBN

3764369957

Enbook ID

01716656

Kiadó

Birkhauser Verlag AG

Súly

2000

Méretek

155 x 235 x 64

Teljes leírás

The book explores the theory of discrete integrable systems, with an emphasis on the following general problem: how to discretize one or several of independent variables in a given integrable system of differential equations, maintaining the integrability property? This question (related in spirit to such a modern branch of numerical analysis as geometric integration) is treated in the book as an immanent part of the theory of integrable systems, also commonly termed as the theory of solitons.§Among several possible approaches to this theory, the Hamiltonian one is chosen as the guiding principle. A self-contained exposition of the Hamiltonian (r-matrix, or "Leningrad") approach to integrable systems is given, culminating in the formulation of a general recipe for integrable discretization of r-matrix hierarchies. After that, a detailed systematic study is carried out for the majority of known discrete integrable systems which can be considered as discretizations of integrable ordinary differential or differential-difference (lattice) equations. This study includes, in all cases, a unified treatment of the correspondent continuous integrable systems as well. The list of systems treated in the book includes, among others: Toda and Volterra lattices along with their numerous generalizations (relativistic, multi-field, Lie-algebraic, etc.), Ablowitz-Ladik hierarchy, peakons of the Camassa-Holm equation, Garnier and Neumann systems with their various relatives, many-body systems of the Calogero-Moser and Ruijsenaars-Schneider type, various integrable cases of the rigid body dynamics. Most of the results are only available from recent journal publications, many of them are new. §Thus, the book is a kind of encyclopedia on discrete integrable systems. It unifies the features of a research monograph and a handbook. It is supplied with an extensive bibliography and detailed bibliographic remarks at the end of each chapter. Largely self-contained, it will be accessible to graduate and post-graduate students as well as to researchers in the area of integrable dynamical systems. Also those involved in real numerical calculations or modelling with integrable systems will find it very helpful.

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Problem of Integrable Discretization

Hamiltonian Approach

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