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 equations.The 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.
Share This Book: