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 been known for some time that many of the familiar integrable systems of equations are symmetry reductions of self-duality equations on a metric or on a Yang-Mills connection (for example, the Korteweg-de Vries and nonlinear Schroedinger equations are reductions of the self-dual Yang-Mills equation). 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 Backlund tranformations, the inverse scattering method, and other such
general constructions of integrability theory, and that it elucidates the connections between them.