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Table of contents (42 chapters)
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Front Matter
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Self-Dual Yang-Mills Equations
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Completely Integrable Equations
About this book
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. Painlevé analysis of partial differential equations, studies of the Painlevé 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 severalarticles 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.
Editors and Affiliations
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Department of Mathematics, University of Exeter, Exeter, UK
Peter A. Clarkson
Bibliographic Information
Book Title: Applications of Analytic and Geometric Methods to Nonlinear Differential Equations
Editors: Peter A. Clarkson
Series Title: Nato Science Series C:
DOI: https://doi.org/10.1007/978-94-011-2082-1
Publisher: Springer Dordrecht
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eBook Packages: Springer Book Archive
Copyright Information: Springer Science+Business Media Dordrecht 1993
Hardcover ISBN: 978-0-7923-2457-7Published: 30 September 1993
Softcover ISBN: 978-94-010-4924-5Published: 13 October 2012
eBook ISBN: 978-94-011-2082-1Published: 06 December 2012
Series ISSN: 1389-2185
Edition Number: 1
Number of Pages: X, 477
Topics: Theoretical, Mathematical and Computational Physics, Mathematical and Computational Engineering, Applications of Mathematics, Partial Differential Equations, Global Analysis and Analysis on Manifolds, Ordinary Differential Equations