Integrable systems : twistors, loop groups, and Riemann surfaces / N.J. Hitchin, G.B. Segal, R.S. Ward.

Format:

Book

Author/Creator:

Hitchin, N. J. (Nigel J.), 1946-

Contributor:

Segal, Graeme.

Woodhouse, N. M. J. (Nicholas Michael John), 1949-

Ward, R. S. (Richard Samuel), 1951-

Series:

Oxford graduate texts in mathematics ; 4.

Oxford graduate texts in mathematics ; 4

Language:

English

Genre:

Conference papers and proceedings.

Physical Description:

viii, 136 pages ; 25 cm.

Place of Publication:

Oxford : Clarendon Press ; New York : Oxford University Press, 1999.

Summary:

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 Schr"odinger 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.

Notes:

"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".

Includes bibliographical references and index.

ISBN:

0198504217

OCLC:

41017726