自旋卡罗热-莫泽体系Bäcklund变换的一致性

Pub Date : 2023-05-08 DOI:10.1007/s11040-023-09450-z

Bjorn K. Berntson

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引用次数: 1

摘要

证明了自旋Calogero-Moser (sCM)系统在有理、三角和双曲情况下Bäcklund变换(BT)的一致性。sCM系统的BT由一个常微分方程的过定系统组成;为了建立我们的结果，我们构造并分析了一些函数来度量这个超定系统与一致性的偏离。我们证明了这些函数是同零的，并且这允许超定系统的初值问题的唯一解。

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Consistency of the Bäcklund Transformation for the Spin Calogero–Moser System

We prove the consistency of the Bäcklund 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 ordinary differential equations; to establish our result, we construct and analyze certain functions that measure the departure of this overdetermined system from consistency. We show that these functions are identically zero and that this allows for a unique solution to the initial value problem for the overdetermined system.

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