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Oxford Graduate Texts in Mathematics #4: Integrable Systems: Twistors, Loop Groups, and Riemann Surfaces

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Oxford Graduate Texts in Mathematics #4: Integrable Systems: Twistors, Loop Groups, and Riemann Surfaces Cover

 

Synopses & Reviews

Publisher 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 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.

Synopsis:

This textbook for graduate students introduces integrable systems through the study of Riemann surfaces, loop groups, and twistors. Topics include Korteweg-de Vries and nonlinear Schrodinger equations, the inverse scattering transform, algebraic curves, and self-dual Yang-Mills equations.

Table of Contents

List 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

Product Details

ISBN:
9780198504214
Author:
Hitchin, N. J.
Author:
Segal, G. B.
Author:
null, N. J.
Author:
null, G. B.
Author:
null, R. S.
Author:
Ward, R. S.
Publisher:
Oxford University Press, USA
Subject:
Differential Equations
Subject:
Number Systems
Subject:
Riemann surfaces
Subject:
Hamiltonian systems
Subject:
Topology - General
Subject:
Mathematics | Applied Mathematics
Subject:
Mathematics-Introduction
Edition Number:
2
Series:
Oxford Graduate Texts in Mathematics
Series Volume:
No. 4
Publication Date:
19990531
Binding:
HARDCOVER
Grade Level:
College/higher education:
Language:
English
Illustrations:
38 b/w illus.
Pages:
152
Dimensions:
9.52x6.34x.56 in. .70 lbs.

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Related Subjects

Education » Phonics
Science and Mathematics » Mathematics » Analysis General
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Oxford Graduate Texts in Mathematics #4: Integrable Systems: Twistors, Loop Groups, and Riemann Surfaces New Hardcover
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Product details 152 pages Oxford University Press - English 9780198504214 Reviews:
"Synopsis" by , This textbook for graduate students introduces integrable systems through the study of Riemann surfaces, loop groups, and twistors. Topics include Korteweg-de Vries and nonlinear Schrodinger equations, the inverse scattering transform, algebraic curves, and self-dual Yang-Mills equations.
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