Nonlinear integrable equations, such as the KdV equation, the Boussine
sq equation and the KP equation, have a close relation with the many-b
ody problem. The solutions of such equations are the same as the restr
icted flows of the classical Calogero model, which is a one-dimensiona
l particle system with inverse square interactions. The KP hierarchy a
nd the Calogero model share the same structure called 'additional symm
etry''. This additional symmetry plays a crucial role in this relation
.