On the geometry of soliton equations

The paper aims to suggest a geometric point of view in the theory of soliton equations. The belief is that a deeper understanding of the origin of these equations may provide a better understanding of their remarkable properties. According to the geometric point of view, soliton equations are the outcome of a specific reduction process of a bi-Hamiltonian manifold. The suggestion of the paper is to pay attention also to the unreduced form of soliton equations.This work has been supported by the Italian MURST and by the GNFM of the Italian CNR.