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Matrix Kadomtsev—Petviashvili Hierarchy and Spin Generalization of Trigonometric Calogero—Moser Hierarchy
Proceedings of the Steklov Institute of Mathematics ( IF 0.4 ) Pub Date : 2020-08-08 , DOI: 10.1134/s0081543820030177 V. V. Prokofev , A. V. Zabrodin
Proceedings of the Steklov Institute of Mathematics ( IF 0.4 ) Pub Date : 2020-08-08 , DOI: 10.1134/s0081543820030177 V. V. Prokofev , A. V. Zabrodin
We consider solutions of the matrix Kadomtsev-Petviashvili (KP) hierarchy that are trigonometric functions of the first hierarchical time t1 = x and establish the correspondence with the spin generalization of the trigonometric Calogero-Moser system at the level of hierarchies. Namely, the evolution of poles xi and matrix residues at the poles a
αi
b
βi
of the solutions with respect to the kth hierarchical time of the matrix KP hierarchy is shown to be given by the Hamiltonian flow with the Hamiltonian which is a linear combination of the first k higher Hamiltonians of the spin trigonometric Calogero-Moser system with coordinates xi and with spin degrees of freedom α
αi
and b
βi
. By considering the evolution of poles according to the discrete time matrix KP hierarchy, we also introduce the integrable discrete time version of the trigonometric spin Calogero-Moser system.
中文翻译:
矩阵Kadomtsev-Petviashvili层次结构和三角Calogero-Moser层次结构的自旋推广
我们考虑矩阵Kadomtsev-Petviashvili(KP)层次结构的解决方案,它们是第一层次时间t 1 = x的三角函数,并在层次结构级别上与三角Calogero-Moser系统的自旋泛化建立了对应关系。即,磁极的进化X我和基质的残基在两极一个α我b β我的解决方案相对于所述ķ矩阵KP层次的第分层时间被示出为通过与哈密顿哈密顿流动,这是给出前k个线性组合 自旋三角函数卡洛杰罗-Moser的系统坐标的更高汉密尔顿X我并与自旋自由度α α我和b β我。通过根据离散时间矩阵KP层次考虑极点的演化,我们还介绍了三角自旋Calogero-Moser系统的可积分离散时间版本。
更新日期:2020-08-08
中文翻译:
矩阵Kadomtsev-Petviashvili层次结构和三角Calogero-Moser层次结构的自旋推广
我们考虑矩阵Kadomtsev-Petviashvili(KP)层次结构的解决方案,它们是第一层次时间t 1 = x的三角函数,并在层次结构级别上与三角Calogero-Moser系统的自旋泛化建立了对应关系。即,磁极的进化X我和基质的残基在两极一个α我b β我的解决方案相对于所述ķ矩阵KP层次的第分层时间被示出为通过与哈密顿哈密顿流动,这是给出前k个线性组合 自旋三角函数卡洛杰罗-Moser的系统坐标的更高汉密尔顿X我并与自旋自由度α α我和b β我。通过根据离散时间矩阵KP层次考虑极点的演化,我们还介绍了三角自旋Calogero-Moser系统的可积分离散时间版本。