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Applications of Analytic and Geometric Methods to Nonlinear Differential Equations : NATO Science Series C - P. A. Clarkson

Applications of Analytic and Geometric Methods to Nonlinear Differential Equations

NATO Science Series C

By: P. A. Clarkson (Editor)

Hardcover

Published: 30th September 1993
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In the study of integrable systems, two different approaches in particular have attracted considerable attention during the past twenty years. (1) The inverse scattering transform (IST), using complex function theory, which has been employed to solve many physically significant equations, the `soliton' equations. (2) Twistor theory, using differential geometry, which has been used to solve the self-dual Yang--Mills (SDYM) equations, a four-dimensional system having important applications in mathematical physics. Both soliton and the SDYM equations have rich algebraic structures which have been extensively studied.
Recently, it has been conjectured that, in some sense, all soliton equations arise as special cases of the SDYM equations; subsequently many have been discovered as either exact or asymptotic reductions of the SDYM equations. Consequently what seems to be emerging is that a natural, physically significant system such as the SDYM equations provides the basis for a unifying framework underlying this class of integrable systems, i.e. `soliton' systems. This book contains several articles on the reduction of the SDYM equations to soliton equations and the relationship between the IST and twistor methods.
The majority of nonlinear evolution equations are nonintegrable, and so asymptotic, numerical perturbation and reduction techniques are often used to study such equations. This book also contains articles on perturbed soliton equations. Painleve analysis of partial differential equations, studies of the Painleve equations and symmetry reductions of nonlinear partial differential equations.


(ABSTRACT)
In the study of integrable systems, two different approaches in particular have attracted considerable attention during the past twenty years; the inverse scattering transform (IST), for `soliton' equations and twistor theory, for the self-dual Yang--Mills (SDYM) equations. This book contains several articles on the reduction of the SDYM equations to soliton equations and the relationship between the IST and twistor methods. Additionally, it contains articles on perturbed soliton equations, Painlevé analysis of partial differential equations, studies of the Painlevé equations and symmetry reductions of nonlinear partial differential equations.

Preface
Self-Dual Yang--Mills Equations
Completely Integrable Equations
PainlevF Equations and PainlevF Analysis
Symmetries of Differential Equations
Author Index
Subject Index
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780792324577
ISBN-10: 0792324579
Series: NATO Science Series C
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 477
Published: 30th September 1993
Publisher: Springer
Country of Publication: NL
Dimensions (cm): 23.5 x 15.5  x 2.69
Weight (kg): 1.89