Integrable Systems: Twistors, Loop Groups, and Riemann Surfaces

Hardcover | January 1, 1999

byN. J. Hitchin, G. B. Segal, R. S. Ward

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This textbook is designed to give graduate students an understanding of integrable systems via the study of Riemann surfaces, loop groups, and twistors. The book has its origins in a series of lecture courses given by the authors, all of whom are internationally known mathematicians andrenowned expositors. It is written in an accessible and informal style, and fills a gap in the existing literature. The introduction by Nigel Hitchin addresses the meaning of integrability: how do we recognize an integrable system? His own contribution then develops connections with algebraicgeometry, and includes an introduction to Riemann surfaces, sheaves, and line bundles. Graeme Segal takes the Kortewegde Vries and nonlinear Schrodinger equations as central examples, and explores the mathematical structures underlying the inverse scattering transform. He explains the roles ofloop groups, the Grassmannian, and algebraic curves. In the final part of the book, Richard Ward explores the connection between integrability and the self-dual Yang-Mills equations, and describes the correspondence between solutions to integrable equations and holomorphic vector bundles overtwistor space.

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This textbook is designed to give graduate students an understanding of integrable systems via the study of Riemann surfaces, loop groups, and twistors. The book has its origins in a series of lecture courses given by the authors, all of whom are internationally known mathematicians andrenowned expositors. It is written in an accessib...

N. J. Hitchin is at University of Oxford. G. B. Segal is at University of Cambridge.

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Format:HardcoverPublished:January 1, 1999Publisher:Oxford University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0198504217

ISBN - 13:9780198504214

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Table of Contents

1. Nigel Hitchin: Introduction2. Nigel Hitchin: Riemann surfaces and integrable systems3. Graeme Segal: Integrable systems and inverse scattering4. Richard Ward: Integrable systems and twistorsIndex

Editorial Reviews

"The lecturers cover an enormous amount of material, ranging from algeraic geometry and the theory of Riemann surfaces to loop groups, connections, Yang-Mills equations and twister theory. However despite this wide range, the book is surprisingly self-contained and readable" Bulletin of theLondon Mathematical Society"