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Other titles in the Oxford Graduate Texts in Mathematics series:
Oxford Graduate Texts in Mathematics #4: Integrable Systems: Twistors, Loop Groups, and Riemann Surfacesby N. J. Hitchin
Synopses & ReviewsPublisher Comments: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 Kortewegde 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 selfdual YangMills equations and then describes the correspondence between solutions to integrable equations and holomorphic vector bundles over twistor space.
Synopsis:This textbook for graduate students introduces integrable systems through the study of Riemann surfaces, loop groups, and twistors. Topics include Kortewegde Vries and nonlinear Schrodinger equations, the inverse scattering transform, algebraic curves, and selfdual YangMills equations.
Table of ContentsList of contributors
1. Introduction, Nigel Hitchin 2. Riemann surfaces and integrable systems, Nigel Hitchin 3. Integrable systems and inverse scattering, Graeme Segal 4. Integrable systems and twistors, Richard Ward Index What Our Readers Are SayingBe the first to add a comment for a chance to win!Product Details
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