Integrability, Self-duality, and Twistor Theory

Hardcover | April 30, 1999

byL. J. Mason, N. M. J. Woodhouse

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It has been known for some time that 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 nonlinear Schr"odinger equations are reductions of the self-dualYang-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 has two central themes: first, that the symmetries of self-duality equations provide a natural classification scheme forintegrable systems; and second that twistor theory provides a uniform geometric framework for the study of B"acklund tranformations, the inverse scattering method, and other such general constructions of integrability theory, and that it elucidates the connections between them.

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It has been known for some time that 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 nonlinear Schr"odinger equations are reductions of the self-dualYang-Mills equation). This book explores in detail ...

L. Mason is at University of Oxford. N. M. J. Woodhouse is at University of Oxford.

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Format:HardcoverDimensions:374 pages, 9.21 × 6.14 × 0.98 inPublished:April 30, 1999Publisher:Oxford University Press

The following ISBNs are associated with this title:

ISBN - 10:0198534981

ISBN - 13:9780198534983

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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 guage transformationsAppendix A. 3 The Drinfeld-Sokolov equations

Editorial Reviews

' This book provides ample food for both mathematical thought and practice, and is recommended reading for all who have some interest in the intriguing notion of integrability'Bulletin London Mathematical Society