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

We consider solutions of the KP hierarchy which are elliptic functions $x=t_1$. It is known that their poles as $t_2$ move particles Calogero-Moser model. extend this correspondence to level hierarchies and find Hamiltonian $H_k$ model governs dynamics with respect $k$-th hierarchical time. The Hamiltonians obtained coefficients expansion spectral curve near marked point in Baker-Akhiezer function has essential singularity.