Elliptic solutions to the KP hierarchy and elliptic Calogero–Moser model

Abstract

We consider solutions of the Kadomtsev–Petviashvili hierarchy which are elliptic functions of x = t 1. It is known that their poles as functions of t 2 move as particles of the elliptic Calogero–Moser model. We extend this correspondence to the level of hierarchies and find the Hamiltonian H k of the elliptic Calogero–Moser model which governs the dynamics of poles with respect to the kth hierarchical time. The Hamiltonians H k are obtained as coefficients of the expansion of the spectral curve near the marked point in which the Baker–Akhiezer function has essential singularity.