Integrability, Self-Duality, and Twistor Theory

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

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
Publication date:	01/30/1997
Series:	London Mathematical Society Monographs , #15
Pages:	376
Product dimensions:	9.21(w) x 6.14(h) x 0.88(d)

About the Author

Mathematical Institute, Oxford

Mathematical Institute, Oxford

Table of Contents

Part I: Self-Duality And Integrable Equations1. Mathematical background2. The self-dual Yang-Mills equations3. Symmetries and reduction4. Reductions to three dimensions5. Reductions to two dimensions6. Reduction to one dimension7. Hierarchies8. Other self-duality equationsPart II: Twistor Theory9. Mathematical background10. Twistor space and the ward construction11. Reductions of the ward construction12. Generalizations of the twistor construction13. Boundary conditions14. Construction of exact solutionsAppendix A. 1 Lifts and invariant connectionsAppendix B. 2 Active and passive gauge transformationsAppendix A. 3 The Drinfeld-Sokolov equations

Editorial Reviews

"This excellently written book should be of interest to two distinct grounps. Geometrists will be able to learn about integrable systems, and, vice-versa, interable theorists will be introduced to the geometry underlying many of their constructions."—Mathematical Reviews

From the Publisher