Integrability, Self-duality, and Twistor Theory

This book explores in detail the connections between self-duality and integrability, and also the application of twistor techniques to integrable systems. It has two central themes: first, that the symmetries of self-duality equations provide a natural classification scheme for integrable systems; and second that twistor theory provides a uniform geometric framework for the study of B¨acklund tranformations, the inverse scattering method, and other such general constructions of integrability theory, and that it elucidates the connections between them.