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KP hierarchy and trigonometric Calogero-Moser hierarchy
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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.
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Elliptic solutions to matrix CKP equation
Elliptic solutions of the matrix CKP equation have pole dynamics described by a first-order system, equations (47)-(48), generalizing the scalar CKP result.
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