Solitons, instantons, and twistors

丛 书 名：Oxford graduate texts in mathematics

作     者：Maciej Dunajski 

I S B N：(纸本) 0198570627;9780198570622;0198570635;9780198570639 

出 版 社：Oxford University Press  USA 

出 版 年：2010年

页      数：xi, 359 p. :页

主 题 词：Twistor theory. Wave-motion Theory of. Geometry Differential. Solitons Mathematics. 

学科分类：0809[工学-电子科学与技术（可授工学、理学学位）] 07[理学] 070205[理学-凝聚态物理] 08[工学] 0702[理学-物理学] 

馆 藏 号：201767520...

摘      要：Most nonlinear differential equations arising in natural sciences admit chaotic behavior and cannot be solved analytically. Integrable systems lie on the other extreme. They possess regular, stable, and well behaved solutions known as solitons and instantons. These solutions play important roles in pure and applied mathematics as well as in theoretical physics where they describe configurations topologically different from vacuum. While integrable equations in lower space-time dimensions can be solved using the inverse scattering transform, the higher-dimensional examples of anti-self-dual Yang-Mills and Einstein equations require twistor theory. Both techniques rely on an ability to represent nonlinear equations as compatibility conditions for overdetermined systems of linear differential *** book provides a self-contained and accessible introduction to the subject. It starts with an introduction to integrability of ordinary and partial differential equations. Subsequent chapters explore symmetry analysis, gauge theory, gravitational instantons, twistor transforms, and anti-self-duality equations. The three appendices cover basic differential geometry, complex manifold theory, and the exterior differential system