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

Vadim Prokofev, A. Zabrodin

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1 Citation (Scopus)

Abstract

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.

Original languageEnglish
Article number305202
JournalJournal of Physics A: Mathematical and Theoretical
Volume54
Issue number30
DOIs
Publication statusPublished - Jul 2021

Keywords

  • Elliptic calogero-moser model
  • Integrable systems
  • Kadomtsev-Petviashvili hierarchy

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