Topics in Soliton Theory (Volume 167) (North-Holland Mathematics Studies, Volume 167)

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. 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