《Integrable Systems》是由N. J. Hitchin、G. B. Segal和R. S. Ward合著的學術專著。該書系統構建了可積系統理論框架，全書分為三部分：第一部分從代數幾何視角探討可積系統的判別標準；第二部分研究可積方程的解空間結構；第三部分闡述量子可積系統的幾何實現方法。該書被列為牛津大學數學研究生核心教材。
基本介紹
- ISBN：9780198504214
- 作者：N. J. Hitchin、G. B. Segal、R. S. Ward
- 出版社：Oxford University Press, USA
- 出版時間：1999年5月13日
- 頁數：152
- 定價：USD 99.00
- 裝幀：Hardcover
- 叢書：Oxford Graduate Texts in Mathematics
內容簡介
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 t...(展開全部) 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.
