Gelfand–Dickey hierarchy, generalized BGW tau-function, and W-constraints. (1st March 2023)

• Record Type: Journal Article
• Authors: Yang, Di; Zhou, Chunhui
• Is Part Of: Nonlinearity. Volume 36:Number 3(2023)
• Page Start: 1873
• Page End: 1889
• Publication Date: 2023-03-01
• Subjects: Gelfand–Dickey hierarchy -- W-constraints -- generalized BGW tau-function -- KP hierarchy; 37K10 -- 35Q53; Nonlinear theories -- Periodicals; Mathematical analysis -- Periodicals; Mathematical analysis; Nonlinear theories; Periodicals; 515
• DOI: 10.1088/1361-6544/acb62c
• Languages: English
• ISSNs: 0951-7715

Abstract

Abstract: Let r ⩾ 2 be an integer. The generalized Brezin–Gross–Witten (BGW) tau-function for the Gelfand–Dickey hierarchy of ( r − 1 ) dependent variables (aka the r -reduced Kadomtsev–Petviashvili hierarchy) is defined as a particular tau-function that depends on ( r − 1 ) constant parameters d 1, …, d r − 1 . In this paper we show that this tau-function satisfies a family of linear equations, called the W -constraints of the second kind. The operators giving rise to the linear equations also depend on ( r − 1 ) constant parameters. We show that there is a one-to-one correspondence between the two sets of parameters.