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

Kazuhiro Hikami·Miki Wadati
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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.

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Kazuhiro Hikami, Miki Wadati. 1994-02-04. On the Additional Symmetry; Many-Body Problem Related to the KP Hierarchy. https://arxiv.org/abs/hep-th/9402026

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