Tetsuji Miwa, M. Jimbo, T. Miwa

Solitons

Differential Equations, Symmetries and Infinite Dimensional Algebras

• Gebundenes Buch

Produktbeschreibung

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.

Table of contents:
1. The KdV equation and its symmetries; 2. The KdV hiearchy; 3. The Hirota equation and vertex operators; 4. The calculus of fermions; 5. The boson-fermion correspondence; 6. Transformation groups and tau functions; 7. Transformation group of the KdV equation; 8. Finite dimensional Grassmanians and Plücker relations; 9. Infinite dimensional Grassmanians; 10. The bilinear identity revisited.

This book investigates the high degree of symmetry that lies hidden in integrable systems. Differential equations arising from classical mechanics, (e.g. the KdV equation and the KP equations), are used to introduce the notion of infinite dimensional transformation groups acting on spaces of integrable systems.

The goal of this book is to investigate the high degree of symmetry that lies hidden in integrable systems.

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Hinweis: Dieser Artikel kann nur an eine deutsche Lieferadresse ausgeliefert werden.

Produktdetails

• Verlag: Cambridge University Press
• Seitenzahl: 122
• Erscheinungstermin: 8. November 2011
• Englisch
• Abmessung: 235mm x 157mm x 11mm
• Gewicht: 341g
• ISBN-13: 9780521561617
• ISBN-10: 0521561612
• Artikelnr.: 21975512

Inhaltsangabe

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.