Author: Robert Hermann
Publisher:
ISBN:
Category :
Languages : en
Pages : 347

Get Book Here

Book Description

Author: Robert Hermann
Publisher:
ISBN:
Category : Mathematical physics
Languages : en
Pages : 376

Get Book Here

Book Description

Author: Stefan Rauch-Wojciechowski
Publisher:
ISBN:
Category :
Languages : en
Pages : 8

Get Book Here

Book Description

Author: Gleb Arutyunov
Publisher: Springer
ISBN: 303024198X
Category : Science
Languages : en
Pages : 414

Get Book Here

Book Description
Integrable models have a fascinating history with many important discoveries that dates back to the famous Kepler problem of planetary motion. Nowadays it is well recognised that integrable systems play a ubiquitous role in many research areas ranging from quantum field theory, string theory, solvable models of statistical mechanics, black hole physics, quantum chaos and the AdS/CFT correspondence, to pure mathematics, such as representation theory, harmonic analysis, random matrix theory and complex geometry. Starting with the Liouville theorem and finite-dimensional integrable models, this book covers the basic concepts of integrability including elements of the modern geometric approach based on Poisson reduction, classical and quantum factorised scattering and various incarnations of the Bethe Ansatz. Applications of integrability methods are illustrated in vast detail on the concrete examples of the Calogero-Moser-Sutherland and Ruijsenaars-Schneider models, the Heisenberg spin chain and the one-dimensional Bose gas interacting via a delta-function potential. This book has intermediate and advanced topics with details to make them clearly comprehensible.

Author: Krzysztof Marciniak
Publisher:
ISBN: 9789172192348
Category :
Languages : en
Pages : 140

Get Book Here

Book Description

Author: Jens Hoppe
Publisher: Springer Science & Business Media
ISBN: 3540472746
Category : Science
Languages : en
Pages : 109

Get Book Here

Book Description
Mainly drawing on explicit examples, the author introduces the reader to themost recent techniques to study finite and infinite dynamical systems. Without any knowledge of differential geometry or lie groups theory the student can follow in a series of case studies the most recent developments. r-matrices for Calogero-Moser systems and Toda lattices are derived. Lax pairs for nontrivial infinite dimensionalsystems are constructed as limits of classical matrix algebras. The reader will find explanations of the approach to integrable field theories, to spectral transform methods and to solitons. New methods are proposed, thus helping students not only to understand established techniques but also to interest them in modern research on dynamical systems.

Author: S. Rauch-Wojciehowski
Publisher:
ISBN:
Category :
Languages : en
Pages : 8

Get Book Here

Book Description

Author: Diarmuid Ó'Mathúna
Publisher: Springer Science & Business Media
ISBN: 0817645950
Category : Science
Languages : en
Pages : 241

Get Book Here

Book Description
Shows that exact solutions to the Kepler (two-body), the Euler (two-fixed center), and the Vinti (earth-satellite) problems can all be put in a form that admits the general representation of the orbits and follows a definite shared pattern Includes a full analysis of the planar Euler problem via a clear generalization of the form of the solution in the Kepler case Original insights that have hithertofore not appeared in book form

Author: Jens Hoppe
Publisher: Springer Science & Business Media
ISBN: 3540557008
Category : Mathematics
Languages : en
Pages : 109

Get Book Here

Book Description
Mainly drawing on explicit examples, the author introduces the reader to themost recent techniques to study finite and infinite dynamical systems. Without any knowledge of differential geometry or lie groups theory the student can follow in a series of case studies the most recent developments. r-matrices for Calogero-Moser systems and Toda lattices are derived. Lax pairs for nontrivial infinite dimensionalsystems are constructed as limits of classical matrix algebras. The reader will find explanations of the approach to integrable field theories, to spectral transform methods and to solitons. New methods are proposed, thus helping students not only to understand established techniques but also to interest them in modern research on dynamical systems.

Author: Costas J. Papachristou
Publisher: Springer Nature
ISBN: 3030350029
Category : Science
Languages : en
Pages : 101

Get Book Here

Book Description
This book serves as an introduction to the concept of integrability as it applies to systems of differential equations as well as to vector-valued fields. The author focuses on specific aspects of integrability that are often encountered in a variety of problems in applied mathematics, physics and engineering. The following general cases of integrability are examined: (a) path-independence of line integrals of vector fields on the plane and in space; (b) integration of a system of ordinary differential equations by using first integrals; and (c) integrable systems of partial differential equations. Special topics include the integration of analytic functions and some elements from the geometric theory of differential systems. Certain more advanced subjects, such as Lax pairs and Bäcklund transformations, are also discussed. The book is written at an intermediate level for educational purposes. The presentation is as simple as the topics allow, often sacrificing mathematical rigor in favor of pedagogical efficiency.