This article is cited in 2 papers

Constrained discrete KP hierarchy: the constraint on the tau functions and gauge transformations

Jia-Qi Song^a, Chong Li^b, Ji-Peng Cheng^c, Min-Ru Chen<sup>a

a</sup> School of Mathematics and Statistics, Henan University, Kaifeng, China
^b School of Mathematics and Statistics, Ningbo University, Ningbo, China
^c School of Mathematics, China University of Mining and Technology, Xuzhou, China

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.

MSC: 35Q51, 37K10, 37K40

Received: 15.08.2022
Revised: 02.10.2022

DOI: 10.4213/tmf10352

 English version: Theoretical and Mathematical Physics, 2023, 214:3, 334–353

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