Buch, Englisch, 376 Seiten, Format (B × H): 161 mm x 240 mm, Gewicht: 728 g
Buch, Englisch, 376 Seiten, Format (B × H): 161 mm x 240 mm, Gewicht: 728 g
ISBN: 978-0-19-853498-3
Verlag: OUP Oxford
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.
Autoren/Hrsg.
Fachgebiete
- Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
- Naturwissenschaften Biowissenschaften Angewandte Biologie Biomathematik
- Naturwissenschaften Physik Physik Allgemein Geschichte der Physik
- Naturwissenschaften Physik Physik Allgemein Experimentalphysik
- Mathematik | Informatik Mathematik Geometrie Algebraische Geometrie
Weitere Infos & Material
- 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
