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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: en
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, Painlevé Geometry and Lie Algebras
Language: en
Pages: 484
Authors: Mark Adler, Pierre van Moerbeke, Pol Vanhaecke
Categories: Mathematics
Type: BOOK - Published: 2013-03-14 - Publisher: Springer Science & Business Media

This Ergebnisse volume is aimed at a wide readership of mathematicians and physicists, graduate students and professionals. The main thrust of the book is to show how algebraic geometry, Lie theory and Painlevé analysis can be used to explicitly solve integrable differential equations and construct the algebraic tori on which
Integrability Theorems for Trigonometric Transforms
Language: en
Pages: 66
Authors: Ralph P.Jr. Boas
Categories: Mathematics
Type: BOOK - Published: 2012-12-06 - Publisher: Springer Science & Business Media

This monograph is areport on the present state of a fairly coherent collection of problems about which a sizeable literature has grown up in recent years. In this literature, some of the problems have, as it happens, been analyzed in great detail, whereas other very similar ones have been treated
Integrability of Nonlinear Systems
Language: en
Pages: 340
Authors: Yvette Kosmann-Schwarzbach, Basil Grammaticos, K.M. Tamizhmani
Categories: Science
Type: BOOK - Published: 2004-02-17 - Publisher: Springer Science & Business Media

The lectures that comprise this volume constitute a comprehensive survey of the many and various aspects of integrable dynamical systems. The present edition is a streamlined, revised and updated version of a 1997 set of notes that was published as Lecture Notes in Physics, Volume 495. This volume will be