Integrable Systems: Twistors, Loop Groups, and Riemann Surfaces (Oxford Graduate Texts in Mathematics, Vol. 4) - Hardcover
Synopsis
This textbook for graduate students introduces integrable systems through the study of Riemann surfaces, loop groups, and twistors. The introduction by Nigel Hitchin addresses the meaning of integrability, discussing in particular how to recognize an integrable system. He then develops connections between integrable systems and algebraic geometry and introduces Riemann surfaces, sheaves, and line bundles. In the next part, Graeme Segal takes the Korteweg-de Vries and nonlinear Schrödinger equations as central examples and discusses the mathematical structures underlying the inverse scattering transform. He also explains loop groups, the Grassmannian, and algebraic curves. In the final part of the book, Richard Ward explores the connection between integrability and self-dual Yang-Mills equations and then describes the correspondence between solutions to integrable equations and holomorphic vector bundles over twistor space.
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About the Author
N. J. Hitchin is Savilian Professor of Geometry, University of Oxford.
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Integrable Systems: Twisters, Loop Groups, and Riemann Surfaces
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Oxford University Press, Oxford, 1999
ISBN 10: 0198504217
ISBN 13: 9780198504214
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Integrable Systems (Hardcover)
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ISBN 10: 0198504217
ISBN 13: 9780198504214
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Hardcover. Condition: new. Hardcover. 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 and renowned 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 ofintegrability: how do we recognize an integrable system? His own contribution then develops connections with algebraic geometry, and includes an introduction to Riemann surfaces, sheaves, and line bundles.Graeme Segal takes the Kortewegde Vries and nonlinear Schroedinger equations as central examples, and explores the mathematical structures underlying the inverse scattering transform. He explains the roles of loop 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 vectorbundles over twistor space. This textbook is designed to give graduate students an understanding of integrable systems via the study of Riemann surfaces, loop groups, and twistors. The authors are internationally renowned both as researchers and expositors, and the book is written in an informal and accessible style. This item is printed on demand. Shipping may be from our Sydney, NSW warehouse or from our UK or US warehouse, depending on stock availability. Seller Inventory # 9780198504214
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Integrable Systems: Twistors, Loop Groups, and Riemann Surfaces (Oxford Graduate Texts in Mathematics, Vol. 4)
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Condition: New. This textbook is designed to give graduate students an understanding of integrable systems via the study of Riemann surfaces, loop groups, and twistors. The authors are internationally renowned both as researchers and expositors, and the book is written in an informal and accessible style. Series: Oxford Graduate Texts in Mathematics. Num Pages: 148 pages, index. BIC Classification: PBK; PBMP; PBP; PH. Category: (U) Tertiary Education (US: College). Dimension: 243 x 166 x 15. Weight in Grams: 374. . 1999. Hardback. . . . . Seller Inventory # V9780198504214
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