Integrable Systems: Twistors, Loop Groups, and Riemann Surfaces (Paperback) (ISBN-13: 9780199676774)

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 Schrodinger 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.

Author: N. J. Hitchin, G. B. Segal, R. S. Ward
ISBN-10: 0199676771
ISBN-13: 9780199676774
Publisher: Oxford University Press, USA
Language: English
Published: 05/05/2013
Pages: 148
Format: Paperback
Weight: 0.55lbs
Size: 9.10h x 6.10w x 0.50d