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.
Reihe
Sprache
Verlagsort
Zielgruppe
Produkt-Hinweis
Illustrationen
Worked examples or Exercises
Maße
Höhe: 229 mm
Breite: 152 mm
Dicke: 7 mm
Gewicht
ISBN-13
978-1-107-40419-9 (9781107404199)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Klassifikation
Autor*in
RIMS, Kyoto University, Japan
Kyoto University, Japan
University of Osaka, Japan
Übersetzung
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 Pluecker relations; 9. Infinite dimensional Grassmannians; 10. The bilinear identity revisited; Solutions to exercises; Bibliography; Index.
