Constrained discrete KP hierarchy: The constraint on the tau functions and gauge transformations
Jia-Qi Songa, Chong Lib, Ji-Peng Chengc, and Min-Ru Chena, *
aSchool of Mathematics and Statistics, Henan University, Kaifeng, China
bSchool of Mathematics and Statistics, Ningbo University, Ningbo, China
cSchool of Mathematics, China University of Mining and Technology, Xuzhou, China
email: *cmr@henu.edu.cn
Received 15 August, 2022
Abstract—
We investigate two topics of the constrained discrete KP hierarchy: the constraint on the tau functions and gauge transformations. For the constrained dKP hierarchy, the constraint on the Lax operator \({(L^k)_{<0}=q\Delta^{-1}r}\) is shown to be equivalent to a constraint on the tau function, which provides another description of the constrained dKP hierarchy. We also find that there are two different choices of the generating functions in gauge transformation operators of the constrained discrete KP hierarchy.
Keywords:
discrete KP hierarchy,
constrained discrete KP hierarchy,
gauge transformation,
tau function
DOI: 10.1134/S0040577923030030