On the Additional Symmetry; Many-Body Problem Related to the KP Hierarchy

TL;DR

This paper explores the deep connection between nonlinear integrable equations like the KP hierarchy and many-body problems, focusing on the role of additional symmetries that unify these systems.

Contribution

It reveals the shared structure called 'additional symmetry' between the KP hierarchy and the Calogero model, advancing understanding of their integrable nature.

Findings

KP hierarchy and Calogero model share 'additional symmetry' structure

Solutions of integrable equations relate to restricted flows of many-body systems

Highlights the role of symmetry in linking nonlinear equations and particle models

Abstract

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