Isospectral flows related to Frobenius-Stickelberger-Thiele polynomials
Isospectral flows related to Frobenius-Stickelberger-Thiele polynomials
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与 Frobenius-Stickelberger-Thiele 多项式相关的等谱流
DOI：
10.1007/s00220-019-03616-z
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发表时间：
2020
影响因子：
2.4
通讯作者：
Zhedanov Alexei
中科院分区：
文献类型：
--
作者：
Chang Xiang-Ke;Hu Xing-Biao;Szmigielski Jacek;Zhedanov Alexei
Spiridonov 等人引入的 Frobenius-Stickelberger-Thiele (FST) 多项式的等谱变形。 （Commun Math Phys 272:139–165, 2007）进行了研究。对于光谱测量变形的特定选择，会产生可积晶格（FST晶格），它实际上是与广义特征值问题相关的等光谱流。在本文的第二部分中，先前在改进的 Camassa-Holm (mCH) Peakon 晶格研究中使用的谱问题根据 FST 多项式以及相关的 FST 多项式进行解释，从而产生从 mCH Peakon 晶格到有限 FST 晶格负流的映射。此外，还指出有限 FST 晶格的简并情况意外地映射到与 Chang 等人研究的二分量 mCH 方程相关的交错 Peakon ODE 系统。 （高级数学 299：1-35，2016 年）。
The isospectral deformations of the Frobenius–Stickelberger–Thiele (FST) polynomials introduced in Spiridonov et al. (Commun Math Phys 272:139–165, 2007) are studied. For a specific choice of the deformation of the spectral measure, one is led to an integrable lattice (FST lattice), which is indeed an isospectral flow connected with a generalized eigenvalue problem. In the second part of the paper the spectral problem used previously in the study of the modified Camassa–Holm (mCH) peakon lattice is interpreted in terms of the FST polynomials together with the associated FST polynomials, resulting in a map from the mCH peakon lattice to a negative flow of the finite FST lattice. Furthermore, it is pointed out that the degenerate case of the finite FST lattice unexpectedly maps to the interlacing peakon ODE system associated with the two-component mCH equation studied in Chang et al. (Adv Math 299:1–35, 2016).