Spin generalization of the Calogero-Moser hierarchy and the matrix KP hierarchy

TL;DR

This paper reveals a deep connection between rational solutions of the matrix KP hierarchy and the spin Calogero-Moser system, showing that the dynamics of poles in the solutions mirror the integrable structure of the spin Calogero-Moser hierarchy.

Contribution

It establishes a correspondence between matrix KP rational solutions and the spin Calogero-Moser system at the hierarchy level, linking their dynamics and integrable structures.

Findings

Rational solutions of matrix KP are isomorphic to spin Calogero-Moser system.

Pole dynamics in matrix KP solutions follow the higher Hamiltonians of the spin Calogero-Moser hierarchy.

The work extends the understanding of integrable systems with spin generalizations.

Abstract

We establish a correspondence between rational solutions to the matrix KP hierarchy and the spin generalization of the Calogero-Moser system on the level of hierarchies. Namely, it is shown that the rational solutions to the matrix KP hierarchy appear to be isomorphic to the spin Calogero-Moser system in a sense that the dynamics of poles of solutions to the matrix KP hierarchy in the higher times is governed by the higher Hamiltonians of the spin Calogero-Moser integrable hierarchy with rational potential.