Discrete versions of some classical integrable systems and factorization of matrix polynomials
Discrete versions of some classical integrable systems and factorization of matrix polynomials
复制标题
DOI：
10.1007/bf02352494
复制
发表时间：
1991-08
影响因子：
2.4
通讯作者：
J. Moser;A. Veselov
中科院分区：
文献类型：
--
作者：
J. Moser;A. Veselov
研究了几个经典可积系统的离散版本，例如高维无力旋转陀螺（欧拉-阿诺德方程）的离散模拟、具有经典自旋的海森堡链和斯蒂菲尔流形上的新离散系统。可积性是在 Lax 对表示的帮助下显示的，该表示是通过某些矩阵多项式的因式分解找到的。动力学的完整描述是用阿贝尔函数给出的；流量在对应于光谱曲线的 Prym 品种上变为线性。该方法也适用于 N 维椭球内部的台球问题。
Discrete versions of several classical integrable systems are investigated, such as a discrete analogue of the higher dimensional force-free spinning top (Euler-Arnold equations), the Heisenberg chain with classical spins and a new discrete system on the Stiefel manifold. The integrability is shown with the help of a Lax-pair representation which is found via a factorization of certain matrix polynomials. The complete description of the dynamics is given in terms of Abelian functions; the flow becomes linear on a Prym variety corresponding to a spectral curve. The approach is also applied to the billiard problem in the interior of anN-dimensional ellipsoid.