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Nato Science Series C:

Applications of Analytic and Geometric Methods to Nonlinear Differential Equations

Editors: Clarkson, P.A. (Ed.)

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  • ISBN 978-94-011-2082-1
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About this book

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. 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 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.

Table of contents (42 chapters)

  • SDYM Hierarchies and Classical Soliton Systems

    Chakravarty, S.

    Pages 1-8

  • Twistor Theory, Self-Duality and Integrability

    Mason, L. J.

    Pages 9-16

  • Twistor Theory and the Schlesinger Equations

    Mason, L. J. (et al.)

    Pages 17-25

  • Soliton Equations and Connections with Self-Dual Curvature

    Mcintosh, I.

    Pages 27-39

  • Smooth Static Solutions of the Einstein/Yang-Mills Equations

    McLeod, J. B.

    Pages 41-45

Buy this book

eBook $419.00
price for USA
  • ISBN 978-94-011-2082-1
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $529.00
price for USA
  • ISBN 978-0-7923-2457-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $529.00
price for USA
  • ISBN 978-94-010-4924-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Applications of Analytic and Geometric Methods to Nonlinear Differential Equations
Editors
  • P.A. Clarkson
Series Title
Nato Science Series C:
Series Volume
413
Copyright
1993
Publisher
Springer Netherlands
Copyright Holder
Springer Science+Business Media Dordrecht
eBook ISBN
978-94-011-2082-1
DOI
10.1007/978-94-011-2082-1
Hardcover ISBN
978-0-7923-2457-7
Softcover ISBN
978-94-010-4924-5
Series ISSN
1389-2185
Edition Number
1
Number of Pages
X, 477
Topics