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

Autor:	V. V. Prokofev, A. V. Zabrodin
Rok vydání:	2020
Předmět:	symbols.namesake Pure mathematics Hierarchy Nonlinear Sciences::Exactly Solvable and Integrable Systems Mathematics (miscellaneous) Discrete time and continuous time Integrable system symbols Trigonometric functions Trigonometry Linear combination Hamiltonian (quantum mechanics) Mathematics
Zdroj:	Proceedings of the Steklov Institute of Mathematics. 309:225-239
ISSN:	1531-8605 0081-5438
DOI:	10.1134/s0081543820030177
Popis:	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 a b 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 α and b . 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.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::22528765b16c218e31841f2784181ecd https://doi.org/10.1134/s0081543820030177 Zobrazit plný text záznamu Full text from SpringerLink