KP hierarchy and trigonometric Calogero-Moser hierarchy

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We consider trigonometric solutions of the Kadomtsev-Petviashvili (KP) hierarchy. It is known that their poles move as particles of the Calogero-Moser model with trigonometric potential. We show that this correspondence can be extended to the level of hierarchies: The evolution of the poles with respect to the kth hierarchical time of the KP hierarchy is governed by a Hamiltonian that is a linear combination of the first k higher Hamiltonians of the trigonometric Calogero-Moser hierarchy.

Original languageEnglish
Article number043502
JournalJournal of Mathematical Physics
Issue number4
Publication statusPublished - 1 Apr 2020


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