In this paper, the relations between three special forms of matrix integrals and their associated integrable differential-difference systems are considered. It turns out that these matrix integrals with special β = 2 and 1, 4 satisfy the differential-difference KP equation, the two-dimensional Toda lattice, the semi-discrete Toda equation and their Pfaffianized systems, respectively.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.