When soliton theory, based on water waves, plasmas, fiber optics etc., was developing in the 1960-1970 era it seemed that perhaps KdV (and a few other equations) were really rather special in the set of all interesting partial differential equations. As it turns out, although integrable systems are still special, the mathematical interaction of integrable systems theory with virtually all branches of mathematics (and with many currently developing areas of theoretical physics) illustrates the importance of this area. This book concentrates on developing the theme of the tau function. KdV and KP equations are treated extensively, with material on NLS and AKNS systems, and in following the tau function theme one is led to conformal field theory, strings, and other topics in physics. The extensive list of references contains about 1000 entries.
Author(s): Robert W. Carroll (Eds.)
Series: North-Holland Mathematics Studies 167
Publisher: Elsevier, Academic Press
Year: 1991
Language: English
Pages: ii-ix, 1-428
Content:
Editor
Page ii
Edited by
Page iii
Copyright page
Page iv
Preface
Pages v-ix
Chapter 1 KdV and KP; Analytic Methods
Pages 1-98
Chapter 2 Systems and Algebraic Methods
Pages 99-203
Chapter 3 Physics
Pages 205-339
Appendix A Differential Geometry and Elementary Hamiltonian Theory
Pages 341-367
Appendix B Riemann Surfaces and Algebraic Curves
Pages 369-396
References Review Article
Pages 397-419
Index
Pages 421-428
