Title:
Solitons : differential equations, symmetries, and infinite dimensional algebras
Personal Author:
Series Title:
Cambridge tracts in mathematics ; 135.
Series:
Cambridge tracts in mathematics ; 135.
Publication Information:
Cambridge ; New York : Cambridge University Press, 2000
Physical Description:
ix, 108 p. : ill. ; 24 cm.
ISBN:
9780521561617
Available:*
Library | Item Barcode | Call Number | Material Type | Item Category 1 | Status |
---|---|---|---|---|---|
Searching... | 30000010275399 | QC174.26.W28 M587 2000 | Open Access Book | Book | Searching... |
On Order
Summary
Summary
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.
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 Plucker relations |
9 Infinite dimensional Grassmanians |
10 The bilinear identity revisited |