In the last ten to fifteen years, there have been many important developments in the theory of integrable equations. This period is marked in particular by the strong impact of soliton theory in many diverse areas of mathematics and physics: for example, algebraic geometry (the solution of the Schottky problem), group theory (the discovery of quantum groups), topology (the connection of Jones polynomials with integrable models), and quantum gravity (the connection of the KdV with matrix models). This book presents a comprehensive overview of these developments.

1 2 V. E. Zakharov and S. Wabnitz 1 L. D. Landau Institute for Theoretical Physics, 2 Kosygin Str., 117334 Moscow, Russia 2 Laboratoire de Physique, University of Bourgogne, 9 avenue A. Savary, 21078 Dijon, France After about a quarter of a century since the first theoretical predictions of op- tical solitons, the industrial application of the optical soliton concept is near to reality in the booming field of modern telecommunications, where the de- mand for high-speed data transmission and routing is of ever-growing. This book contains a set of lectures that were presented at a Les Houches...

In the last ten to fifteen years there have been many important developments in the theory of integrable equations. This period is marked in particular by the strong impact of soliton theory in many diverse areas of mathematics and physics; for example, algebraic geometry (the solution of the Schottky problem), group theory (the discovery of quantum groups), topology (the connection of Jones polynomials with integrable models), and quantum gravity (the connection of the KdV with matrix models). This is the first book to present a comprehensive overview of these developments. Numbered among...