Solitons
Differential Equations, Symmetries and Infinite Dimensional Algebras

This book was first published in 1999 and investigates the high degree of symmetry that lies hidden in integrable systems.

T. Miwa (Author), M. Jimbo (Author), E. Date (Author), Miles Reid (Translated by)

9780521561617, Cambridge University Press

Hardback, published 2 December 1999

122 pages
22.9 x 15.2 x 1.1 cm, 0.35 kg

This book was first published in 1999 and 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.

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.

Subject Areas: Topology [PBP], Geometry [PBM], Integral calculus & equations [PBKL], Differential calculus & equations [PBKJ]