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What Is Integrability?

Author: Vladimir E. Zakharov

Publisher: Springer Science & Business Media

ISBN: 9783642887031

Category: Science

Page: 321

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The idea of devoting a complete book to this topic was born at one of the Workshops on Nonlinear and Turbulent Processes in Physics taking place reg ularly in Kiev. With the exception of E. D. Siggia and N. Ercolani, all authors of this volume were participants at the third of these workshops. All of them were acquainted with each other and with each other's work. Yet it seemed to be somewhat of a discovery that all of them were and are trying to understand the same problem - the problem of integrability of dynamical systems, primarily Hamiltonian ones with an infinite number of degrees of freedom. No doubt that they (or to be more exact, we) were led to this by the logical process of scientific evolution which often leads to independent, almost simultaneous discoveries. Integrable, or, more accurately, exactly solvable equations are essential to theoretical and mathematical physics. One could say that they constitute the "mathematical nucleus" of theoretical physics whose goal is to describe real clas sical or quantum systems. For example, the kinetic gas theory may be considered to be a theory of a system which is trivially integrable: the system of classical noninteracting particles. One of the main tasks of quantum electrodynamics is the development of a theory of an integrable perturbed quantum system, namely, noninteracting electromagnetic and electron-positron fields.
What Is Integrability?
Language: un
Pages: 321
Authors: Vladimir E. Zakharov
Categories: Science
Type: BOOK - Published: 2012-12-06 - Publisher: Springer Science & Business Media

The idea of devoting a complete book to this topic was born at one of the Workshops on Nonlinear and Turbulent Processes in Physics taking place reg ularly in Kiev. With the exception of E. D. Siggia and N. Ercolani, all authors of this volume were participants at the third
Integrability
Language: en
Pages: 339
Authors: Alexander Mikhailov
Categories: Science
Type: BOOK - Published: 2008-11-25 - Publisher: Springer Science & Business Media

The principal aim of the book is to give a comprehensive account of the variety of approaches to such an important and complex concept as Integrability. Dev- oping mathematical models, physicists often raise the following questions: whether the model obtained is integrable or close in some sense to an integrable
Algebraic Integrability, Painleve Geometry and Lie Algebras
Language: en
Pages: 483
Authors: Mark Adler
Categories: Differential equations
Type: BOOK - Published: 2004 - Publisher:

Books about Algebraic Integrability, Painleve Geometry and Lie Algebras
Hamiltonian Systems and Their Integrability
Language: en
Pages: 149
Authors: Mich'le Audin
Categories: Mathematics
Type: BOOK - Published: 2008 - Publisher: American Mathematical Soc.

Hamiltonian systems began as a mathematical approach to the study of mechanical systems. As the theory developed, it became clear that the systems that had a sufficient number of conserved quantities enjoyed certain remarkable properties. These are the completely integrable systems. In time, a rich interplay arose between integrable systems
Integrability
Language: un
Pages: 339
Authors: Alexander Mikhailov
Categories: Science
Type: BOOK - Published: 2008-11-05 - Publisher: Springer

The principal aim of the book is to give a comprehensive account of the variety of approaches to such an important and complex concept as Integrability. Dev- oping mathematical models, physicists often raise the following questions: whether the model obtained is integrable or close in some sense to an integrable