Integrability, Self-Duality, and Twistor Theory

Integrability, Self-Duality, and Twistor Theory

by L. J. Mason, N. M. J. Woodhouse
     
 

ISBN-10: 0198534981

ISBN-13: 9780198534983

Pub. Date: 01/30/1997

Publisher: Oxford University Press, USA

Many of the familiar integrable systems of equations are symmetry reductions of self-duality equations on a metric or on a Yang-Mills connection. For example, the Korteweg-de Vries and non-linear Schrodinger equations are reductions of the self-dual Yang-Mills equation. This book explores in detail the connections between self-duality and integrability, and also

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Overview

Many of the familiar integrable systems of equations are symmetry reductions of self-duality equations on a metric or on a Yang-Mills connection. For example, the Korteweg-de Vries and non-linear Schrodinger equations are reductions of the self-dual Yang-Mills equation. This book explores in detail the connections between self-duality and integrability, and also the application of twistor techniques to integrable systems. It supports two central theories: that the symmetries of self-duality equations provide a natural classification scheme for integrable systems; and that twistor theory provides a uniform geometric framework for the study of Backlund transformations, the inverse scattering method, and other such general constructions of integrability theory. The book will be useful to researchers and graduate students in mathematical physics.

Product Details

ISBN-13:
9780198534983
Publisher:
Oxford University Press, USA
Publication date:
01/30/1997
Series:
London Mathematical Society Monographs Series, #15
Pages:
376
Product dimensions:
6.38(w) x 9.50(h) x 1.00(d)

Table of Contents

Part I: Self-Duality And Integrable Equations
1. Mathematical background
2. The self-dual Yang-Mills equations
3. Symmetries and reduction
4. Reductions to three dimensions
5. Reductions to two dimensions
6. Reduction to one dimension
7. Hierarchies
8. Other self-duality equations
Part II: Twistor Theory
9. Mathematical background
10. Twistor space and the ward construction
11. Reductions of the ward construction
12. Generalizations of the twistor construction
13. Boundary conditions
14. Construction of exact solutions
Appendix A. 1 Lifts and invariant connections
Appendix B. 2 Active and passive gauge transformations
Appendix A. 3 The Drinfeld-Sokolov equations

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