ON ADDITIONAL SYMMETRY - THE MANY-BODY PROBLEM RELATED TO THE KP HIERARCHY

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 .