• Corpus ID: 203610385

Matrix KP hierarchy and spin generalization of trigonometric Calogero-Moser hierarchy

@article{Prokofev2019MatrixKH,
  title={Matrix KP hierarchy and spin generalization of trigonometric Calogero-Moser hierarchy},
  author={V. Prokofev and A. Zabrodin},
  journal={arXiv: Mathematical Physics},
  year={2019}
}

• V. Prokofev, A. Zabrodin
• Published 29 September 2019
• Mathematics
• arXiv: Mathematical Physics

We consider solutions of the matrix KP hierarchy that are trigonometric functions of the first hierarchical time $t_1=x$ and establish the correspondence with the spin generalization of the trigonometric Calogero-Moser system on the level of hierarchies. Namely, the evolution of poles $x_i$ and matrix residues at the poles $a_i^{\alpha}b_i^{\beta}$ of the solutions with respect to the $k$-th hierarchical time of the matrix KP hierarchy is shown to be given by the Hamiltonian flow with the Hamiltonian which is a linear combination of the first $k$ higher Hamiltonians of the spin trigonometric Calogero-Moser system with coordinates $x_i$ and with spin degrees of freedom $a_i^{\alpha}, \, b_i^{\beta}$. By considering evolution of poles according to the discrete time matrix KP hierarchy we also introduce the integrable discrete time version of the trigonometric spin Calogero-Moser system.