Gordoa, Pilar RPickering, AndrewWattis, Jonathan A D2024-12-022024-12-022021Physica D 415 (2021) 132754Pilar R. Gordoa, Andrew Pickering, Jonathan A.D. Wattis, Integrability and asymptotic behaviour of a differential-difference matrix equation, Physica D: Nonlinear Phenomena, Volume 415, 2021, 132754, ISSN 0167-2789, https://doi.org/10.1016/j.physd.2020.1327540167-2789https://hdl.handle.net/10115/42252The authors are grateful to the Ministry of Economy and Competitiveness of Spain for supporting their work through contract MTM2016-80276-P (AEI/FEDER, EU).In this paper we consider the matrix lattice equation U_{n,t}(U_{n+1} − U_{n−1}) = g(n)I, in both its autonomous (g(n) = 2) and nonautonomous (g(n) = 2n − 1) forms. We show that each of these two matrix lattice equations are integrable. In addition, we explore the construction of Miura maps which relate these two lattice equations, via intermediate equations, to matrix analogs of autonomous and nonautonomous Volterra equations, but in two matrix dependent variables. For these last systems, we consider cases where the dependent variables belong to certain special classes of matrices, and obtain integrable coupled systems of autonomous and nonautonomous lattice equations and corresponding Miura maps. Moreover, in the nonautonomous case we present a new integrable nonautonomous matrix Volterra equation, along with its Lax pair. Asymptotic reductions to the matrix potential Korteweg-de Vries and matrix Korteweg-de Vries equations are also given.engAttribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/integrabilityasymptoticsmatrix equationsdifferential-difference equationsinfo:eu-repo/semantics/article10.1016/j.physd.2020.132754info:eu-repo/semantics/Preprint