Integrability, Self-duality, and Twistor Theory by L. J. Mason

Integrability, Self-duality, and Twistor Theory

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

Hardcover | April 30, 1999

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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.

About The Author

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

Title:Integrability, Self-duality, and Twistor TheoryFormat: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