We consider solutions of the Kadomtsev-Petviashvili hierarchy which are elliptic functions of x = t1. It is known that their poles as functions of t2 move as particles of the elliptic Calogero-Moser model. We extend this correspondence to the level of hierarchies and find the Hamiltonian Hk of the elliptic Calogero-Moser model which governs the dynamics of poles with respect to the kth hierarchical time. The Hamiltonians Hk are obtained as coefficients of the expansion of the spectral curve near the marked point in which the Baker-Akhiezer function has essential singularity.
|Journal||Journal of Physics A: Mathematical and Theoretical|
|Publication status||Published - Jul 2021|
- Elliptic calogero-moser model
- Integrable systems
- Kadomtsev-Petviashvili hierarchy