Matrix Kadomtsev—Petviashvili Hierarchy and Spin Generalization of Trigonometric Calogero

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

Proceedings of the Steklov Institute of Mathematics. 2020. Vol. 309. P. 225–239.

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 aαibβi 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 ααi and bβi. 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.

Research target: Mathematics Physics

Language: English

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Keywords: matrix KP hierarchy

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