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arXiv · 2102.03784

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

V. Prokofev·A. Zabrodin
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Abstract

We consider solutions of the KP 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 $k$-th 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.

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V. Prokofev, A. Zabrodin. 2021-02-07. Elliptic solutions to the KP hierarchy and elliptic Calogero-Moser model. https://doi.org/10.1088/1751-8121%2Fac0a31

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