Integrable systems : twistors, loop groups, and Riemann surfaces : based on lectures given at a conference on integrable systems organized by N.M.J. Woodhouse and held at the Mathematical Institute, University of Oxford, in September 1997

書誌事項

Integrable systems : twistors, loop groups, and Riemann surfaces : based on lectures given at a conference on integrable systems organized by N.M.J. Woodhouse and held at the Mathematical Institute, University of Oxford, in September 1997

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

(Oxford graduate texts in mathematics, 4)

Oxford University Press, 2013

  • : Pbk

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注記

Originally published: Oxford : Clarendon Press, 1999

This edition previously published in hardback: Oxford : Oxford University Press, 2011

内容説明・目次

内容説明

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 of integrability: 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 vector bundles over twistor space.

目次

  • 1. Introduction
  • 2. Riemann surfaces and integrable systems
  • 3. Integrable systems and inverse scattering
  • 4. Integrable systems and twistors
  • Index

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