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基本説明
New in paperback. Hardcover was published in 2000. The main theme of this book is to involve ideas from other areas of mathematics such as algebraic geometry, topology, and in particular infinite dimensional Lie algebras.
Full Description
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.
Contents
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.
