Physics-Mechanics: Nonlinear dynamics and chaos

What is integrability?

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Title (user) : What is integrability?ISBN : 0387519645,9780387519647DDC : 530.1/55353LCC : QC20.7.D5 W43 1990GoogleBook ID : 15LvAAAAMAAJOpenLibrary ID : OL1877956MSeries : Springer series in nonlinear dynamicsAuthors (user) : V. E. ZakharovAuthors (google) : Vladimir Evgen...
Description

Title (user) : What is integrability?

ISBN : 0387519645,9780387519647

DDC : 530.1/55353

LCC : QC20.7.D5 W43 1990

GoogleBook ID : 15LvAAAAMAAJ

OpenLibrary ID : OL1877956M

Series : Springer series in nonlinear dynamics

Authors (user) : V. E. Zakharov

Authors (google) : Vladimir Evgenévich Zakharov

Publisher : Springer-Verlag

Language : English

Publication Date : 1991

Scanned : yes (300 DPI)

File Format : djvu

Categories : Mathematics


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Description (user) :
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: 1. a presentation of the various recently elaborated methods for determining whether a given system is integrable or not; 2. to understand 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 Painlevé test for ordinary (Ercolani, Siggia) and partial differential (Newell, Tabor) equations; the theory of integrable maps in a plane (Veselov); and the theory of the KdV equation with non-vanishing boundary conditions at infinity (Marchenko).


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Description (google) :
This is both a textbook and a monograph. It is partially based on a two-semester course, held by the author for third-year students in physics and mathematics at the University of Salerno, on analytical mechanics, differential geometry, symplectic manifolds and integrable systems.As a textbook, it provides a systematic and self-consistent formulation of Hamiltonian dynamics both in a rigorous coordinate language and in the modern language of differential geometry. It also presents powerful mathematical methods of theoretical physics, especially in gauge theories and general relativity.As a monograph, the book deals with the advanced research topic of completely integrable dynamics, with both finitely and infinitely many degrees of freedom, including geometrical structures of solitonic wave equations.

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