R‐matrix construction of electromagnetic models for the Painlevé transcendents
R‐matrix construction of electromagnetic models for the Painlevé transcendents
复制标题
Painlevé 超越者电磁模型的 R 矩阵构造
DOI：
--
复制
发表时间：
1994
期刊：
影响因子：
--
通讯作者：
M. Routhier
中科院分区：
文献类型：
--
作者：
J. Harnad;M. Routhier
Painleve 超越项 PI-PV 及其作为等单向变形方程的表示是从循环代数 slR(2) 的对偶空间 slR*(2) 上的经典 R 矩阵泊松括号结构导出为非自治哈密顿系统。哈密顿量是通过将 slR*(2) 上谱不变函数的泊松通勤环的元素与时间相关的泊松图族（其图像是 slR*(2) 中的四维有理共交轨道）组合而获得的。每个系统都可以被解释为描述在存在时变电磁场的情况下在零曲率表面上移动的粒子。 Painleve 方程是通过谱不变量环中的第二个交换元素生成的哈密顿流对这些系统进行简化得出的。 © 1995 美国物理研究所。
The Painleve transcendents PI–PV and their representations as isomonodromic deformation equations are derived as nonautonomous Hamiltonian systems from the classical R‐matrix Poisson bracket structure on the dual space slR*(2) of the loop algebra slR(2). The Hamiltonians are obtained by composing elements of the Poisson commuting ring of spectral invariant functions on slR*(2) with a time‐dependent family of Poisson maps whose images are four‐dimensional rational coadjoint orbits in slR*(2). Each system may be interpreted as describing a particle moving on a surface of zero curvature in the presence of a time‐varying electromagnetic field. The Painleve equations follow from reduction of these systems by the Hamiltonian flow generated by a second commuting element in the ring of spectral invariants. © 1995 American Institute of Physics.