Overview

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 Schrödinger 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 has two central themes: first, that the symmetries of self-duality equations provide a natural classification scheme for integrable 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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9780198534983

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Anybody working in integrable systems or in twistor constructions will want a copy of this book or at least want it in their Library. * Proceedings of the Edinburgh Mathematical Society 1998, 41 *

This excellently written book should be of interest to two distinct groups. Geometers will be able to learn about integrable systems, and vice versa, integrable theorists will be introduced to the geometry underlying many of their constructions. ' 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

Anybody working in integrable systems or in twistor constructions will want a copy of this book or at least want it in their Library. Proceedings of the Edinburgh Mathematical Society 1998, 41

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