Consistency of the B\"acklund transformation for the spin Calogero-Moser system
Exactly Solvable and Integrable Systems
2023-05-24 v1 Mathematical Physics
math.MP
Abstract
We prove the consistency of the B\"{a}cklund transformation (BT) for the spin Calogero-Moser (sCM) system in the rational, trigonometric, and hyperbolic cases. The BT for the sCM system consists of an overdetermined system of ODEs; to establish our result, we construct and analyze certain functions that measure the departure of this overdetermined system from consistency and show, under mild assumptions, that these functions are identically zero and that this allows for a unique solution to the initial value problem for the overdetermined system.
Keywords
Cite
@article{arxiv.2207.05002,
title = {Consistency of the B\"acklund transformation for the spin Calogero-Moser system},
author = {Bjorn K. Berntson},
journal= {arXiv preprint arXiv:2207.05002},
year = {2023}
}
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14 pages