Matrix Kadomtsev—Petviashvili Hierarchy and Spin Generalization of Trigonometric Calogero—Moser Hierarchy

V. V. Prokofev, A. V. Zabrodin

Research output: Contribution to journalArticlepeer-review

Abstract

We consider solutions of the matrix Kadomtsev-Petviashvili (KP) hierarchy that are trigonometric functions of the first hierarchical time t1 = x and establish the correspondence with the spin generalization of the trigonometric Calogero-Moser system at the level of hierarchies. Namely, the evolution of poles xi and matrix residues at the poles aiαbiβ of the solutions with respect to the kth 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 xi and with spin degrees of freedom αiα and biβ. By considering the 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.

Original languageEnglish
Pages (from-to)225-239
Number of pages15
JournalProceedings of the Steklov Institute of Mathematics
Volume309
Issue number1
DOIs
Publication statusPublished - 1 May 2020
Externally publishedYes

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