Important Developments in Soliton Theory

This volume provides an overview of recent developments in soliton theory and the theory of integrable equations. It explores the strong impact of soliton theory on diverse areas of mathematics and physics, such as algebraic geometry, group theory, topology and quantum gravity.

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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.