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Zusatztext Anybody working in integrable systems or in twistor constructions will want a copy of this book or at least want it in their Library. Klappentext 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 non-linear Schrodinger 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 supports two central theories: that the symmetries of self-duality equations provide a natural classification scheme for integrable systems; and that twistor theory provides a uniform geometric framework for the study of Backlund transformations, the inverse scattering method, and other such general constructions of integrability theory. The book will be useful to researchers and graduate students in mathematical physics. Zusammenfassung 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 Schrödinger 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. Inhaltsverzeichnis Part I: Self-Duality And Integrable Equations 1: Mathematical background 2: The self-dual Yang-Mills equations 3: Symmetries and reduction 4: Reductions to three dimensions 5: Reductions to two dimensions 6: Reduction to one dimension 7: Hierarchies 8: Other self-duality equations Part II: Twistor Theory 9: Mathematical background 10: Twistor space and the ward construction 11: Reductions of the ward construction 12: Generalizations of the twistor construction 13: Boundary conditions 14: Construction of exact solutions Appendix A. 1 Lifts and invariant connections Appendix B. 2 Active and passive guage transformations Appendix A. 3 The Drinfeld-Sokolov equations ...
