KP hierarchy and trigonometric Calogero-Moser hierarchy

Abstract

We consider trigonometric solutions of the 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 $k$-th hierarchical time of the KP hierarchy is governed by a Hamiltonian which is a linear combination of the first $k$ higher Hamiltonians of the trigonometric Calogero-Moser hierarchy.

arXiv comment17 pages

References in corpus (6)

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• Integrable hydrodynamics of Calogero-Sutherland model: Bidirectional Benjamin-Ono equation
• Calogero-Moser hierarchy and KP hierarchy
• Elliptic solutions to integrable nonlinear equations and many-body systems
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• Elliptic solutions to Toda lattice hierarchy and elliptic Ruijsenaars-Schneider model
• A convergence framework for Airy${}_{\beta }$ line ensemble via pole evolution