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 the authors are many of the most prominent researchers in the
field.
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