Buch, Englisch, Band 135, 122 Seiten, Format (B × H): 157 mm x 235 mm, Gewicht: 339 g
Differential Equations, Symmetries and Infinite Dimensional Algebras
Buch, Englisch, Band 135, 122 Seiten, Format (B × H): 157 mm x 235 mm, Gewicht: 339 g
Reihe: Cambridge Tracts in Mathematics
ISBN: 978-0-521-56161-7
Verlag: Cambridge University Press
This book investigates the high degree of symmetry that lies hidden in integrable systems. To that end, differential equations arising from classical mechanics, such as the KdV equation and the KP equations, are used here by the authors to introduce the notion of an infinite dimensional transformation group acting on spaces of integrable systems. The work of M. Sato on the algebraic structure of completely integrable systems is discussed, together with developments of these ideas in the work of M. Kashiwara. This book should be accessible to anyone with a knowledge of differential and integral calculus and elementary complex analysis, and it will be a valuable resource to the novice and expert alike.
Fachgebiete
- Mathematik | Informatik Mathematik Mathematische Analysis Harmonische Analysis, Fourier-Mathematik
- Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
- Mathematik | Informatik Mathematik Mathematische Analysis Integralrechnungen- und -gleichungen
- Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
Weitere Infos & Material
Preface
1. The KdV equation and its symmetries
2. The KdV hierarchy
3. The Hirota equation and vertex operators
4. The calculus of Fermions
5. The Boson–Fermion correspondence
6. Transformation groups and tau functions
7. The transformation group of the KdV equation
8. Finite dimensional Grassmannians and Plücker relations
9. Infinite dimensional Grassmannians
10. The bilinear identity revisited
Solutions to exercises
Bibliography
Index.
