TY - JOUR

T1 - Matrix Kadomtsev—Petviashvili Hierarchy and Spin Generalization of Trigonometric Calogero—Moser Hierarchy

AU - Prokofev, V. V.

AU - Zabrodin, A. V.

N1 - Funding Information:
The work of A. V. Zabrodin (Sections 2–4) is supported by the Russian Science Foundation under grant 19-11-00062 and performed in Steklov Mathematical Institute of Russian Academy of Sciences.
Publisher Copyright:
© 2020, Pleiades Publishing, Ltd.
Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2020/5/1

Y1 - 2020/5/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85089071917&partnerID=8YFLogxK

U2 - 10.1134/S0081543820030177

DO - 10.1134/S0081543820030177

M3 - Article

AN - SCOPUS:85089071917

VL - 309

SP - 225

EP - 239

JO - Proceedings of the Steklov Institute of Mathematics

JF - Proceedings of the Steklov Institute of Mathematics

SN - 0081-5438

IS - 1

ER -