Letters in Mathematical Physics ( IF 1.2 ) Pub Date : 2023-12-15 , DOI: 10.1007/s11005-023-01745-0 Ang Fu , Di Yang , Dafeng Zuo
In this paper, we extend the matrix-resolvent method to the study of the Dubrovin–Zhang type tau-functions for the constrained KP hierarchy and the bigraded Toda hierarchy of (M, 1)-type. We show that the Dubrovin–Zhang type tau-function of an arbitrary solution to the bigraded Toda hierarchy of (M, 1)-type is a Dubrovin–Zhang type tau-function for the constrained KP hierarchy, which generalizes the result in Carlet et al. (Mosc Math J 4:313–332, 2004) and Fu and Yang (J Geom Phys 179:104592, 2022) for the Toda lattice hierarchy and the NLS hierarchy corresponding to the \(M=1\) case.
中文翻译:
(M,1)型约束KP层次和二级Toda层次
在本文中,我们将矩阵求解方法扩展到约束 KP 层次结构和 (M, 1) 型双分级 Toda 层次结构的 Dubrovin-Zhang 型 tau 函数的研究。我们证明 (M, 1) 型双分级 Toda 层次结构的任意解的 Dubrovin-Zhang 型 tau 函数是约束 KP 层次结构的 Dubrovin-Zhang 型 tau 函数,这概括了 Carlet 等人中的结果等人。 (Mosc Math J 4:313–332, 2004) 以及 Fu 和 Yang (J Geom Phys 179:104592, 2022) 对于 Toda 晶格层次结构和对应于 \(M=1\) 情况的 NLS 层次结构。