What is Integrability? (Springer Series in Nonlinear Dynamics) - Hardcover

 
9783540519645: What is Integrability? (Springer Series in Nonlinear Dynamics)
Hardcover
ISBN 10: 3540519645 ISBN 13: 9783540519645
Verlag: Springer-Verlag Berlin and Heidelberg GmbH & Co. K, 1991

Inhaltsangabe

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.

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Reseña del editor

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.

Reseña del editor

This monograph deals with integrable dynamic systems with an infinite number of degrees of freedom. Leading scientists were invited to discuss the notion of integrability with two main points in mind: a presentation of the various recently elaborated methods for determining whether a given system is integrable or not, and an understanding of the increasingly more important role of integrable systems in modern applied mathematics and theoretical physics. Topics dealt with include: the applicability and integrability of "universal" nonlinear wave models (Calogero); perturbation theory for translational invariant nonlinear Hamiltonian systems (in 2+1d) with an additional integral of motion (Zakharov, Schulman); the role of the Painleve test for ordinary (Ercolani, Siggia) and partial differential (Newell, Tabor) equations; the theory of integrable maps in a plane (Veselov); and the theory of KdV equation with non-vanishing boundary conditions at infinity (Marchenko).

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Verlag
Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Erscheinungsdatum
1991
Sprache
Englisch
ISBN 10 
3540519645
ISBN 13 
9783540519645
Einband
Tapa dura
Anzahl der Seiten
335
Herausgeber
Zakharov V. E., Zakharov Vladimir E.
Kontakt zum Hersteller
Nicht verfügbar
Verantwortliche Person
Nicht verfügbar

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