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Progress in Mathematics

The Problem of Integrable Discretization

Hamiltonian Approach

Authors: Suris, Yuri B.

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eBook 106,99 €
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  • ISBN 978-3-0348-8016-9
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Hardcover 187,19 €
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  • ISBN 978-3-7643-6995-8
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Softcover 135,19 €
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About this book

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.

Table of contents (27 chapters)

Table of contents (27 chapters)

Buy this book

eBook 106,99 €
price for Spain (gross)
  • ISBN 978-3-0348-8016-9
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 187,19 €
price for Spain (gross)
  • ISBN 978-3-7643-6995-8
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
  • The final prices may differ from the prices shown due to specifics of VAT rules
Softcover 135,19 €
price for Spain (gross)
  • ISBN 978-3-0348-9404-3
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
The Problem of Integrable Discretization
Book Subtitle
Hamiltonian Approach
Authors
Series Title
Progress in Mathematics
Series Volume
219
Copyright
2003
Publisher
Birkhäuser Basel
Copyright Holder
Springer Basel AG
eBook ISBN
978-3-0348-8016-9
DOI
10.1007/978-3-0348-8016-9
Hardcover ISBN
978-3-7643-6995-8
Softcover ISBN
978-3-0348-9404-3
Series ISSN
0743-1643
Edition Number
1
Number of Pages
MLXX, 21
Topics