Integrable Systems: Twistors, Loop Groups, and Riemann

Integrable Systems: Twistors, Loop Groups, and Riemann Surfaces (Oxford Graduate Texts in Mathematics)

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.

Country	USA
Binding	Paperback
Brand	Brand: Oxford University Press, USA
EAN	9780199676774
Edition	1
Feature	Used Book in Good Condition
ISBN	0199676771
Label	Oxford University Press
Manufacturer	Oxford University Press
NumberOfItems	1
NumberOfPages	148
PublicationDate	2013-05-05
Publisher	Oxford University Press
Studio	Oxford University Press
ReleaseDate	0000-00-00

Integrable Systems: Twistors, Loop Groups, and Riemann Surfaces (Oxford Graduate Texts in Mathematics)