Download or read book Integrability, Self-duality, and Twistor Theory written by Lionel J. Mason and published by Oxford University Press. This book was released on 1996 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 Schr ̈ odinger 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 B ̈ acklund tranformations, the inverse scattering method, and other such general constructions of integrability theory, and that it elucidates the connections between them.