Abstract
Nonlinear integrable equations, such as the KdV equation, the Boussinesq equation and the KP equation, have a close relation with the many-body problem. The solutions of such equations are the same as the restricted flows of the classical Calogero model, which is a one-dimensional particle system with inverse square interactions. The KP hierarchy and the Calogero model share the same structure called “additional symmetry”. This additional symmetry plays a crucial role in this relation.
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