Spin generalization of the Calogero-Moser hierarchy and the matrix KP hierarchy

Abstract

We establish a correspondence between rational solutions to the matrix KP hierarchy and the spin generalization of the Calogero-Moser system on the level of hierarchies. Namely, it is shown that the rational solutions to the matrix KP hierarchy appear to be isomorphic to the spin Calogero-Moser system in a sense that the dynamics of poles of solutions to the matrix KP hierarchy in the higher times is governed by the higher Hamiltonians of the spin Calogero-Moser integrable hierarchy with rational potential.

17 pages, a reference added

References in corpus (2)

• Universal Whitham hierarchy, dispersionless Hirota equations and multi-component KP hierarchy
• D-Bundles and Integrable Hierarchies

Cited by in corpus (4)

• Multi-solitons of the half-wave maps equation and Calogero-Moser spin-pole dynamics
• Time discretization of the spin Calogero-Moser model and the semi-discrete matrix KP hierarchy
• Elliptic solutions to matrix KP hierarchy and spin generalization of elliptic Calogero-Moser model
• Matrix KP hierarchy and spin generalization of trigonometric Calogero-Moser hierarchy