Integrability and asymptotic behaviour of a differential-difference matrix equation

dc.contributor.authorGordoa, Pilar R
dc.contributor.authorPickering, Andrew
dc.contributor.authorWattis, Jonathan A D
dc.date.accessioned2024-12-02T14:30:52Z
dc.date.available2024-12-02T14:30:52Z
dc.date.issued2021
dc.descriptionThe authors are grateful to the Ministry of Economy and Competitiveness of Spain for supporting their work through contract MTM2016-80276-P (AEI/FEDER, EU).es
dc.description.abstractIn 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.es
dc.identifier.citationPhysica D 415 (2021) 132754es
dc.identifier.citationPilar 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.2020.132754
dc.identifier.doi10.1016/j.physd.2020.132754es
dc.identifier.issn0167-2789
dc.identifier.urihttps://hdl.handle.net/10115/42252
dc.language.isoenges
dc.publisherElsevieres
dc.rightsAttribution-NonCommercial-NoDerivatives 4.0 Internacional*
dc.rights.accessRightsinfo:eu-repo/semantics/Preprintes
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/4.0/*
dc.subjectintegrabilityes
dc.subjectasymptoticses
dc.subjectmatrix equationses
dc.subjectdifferential-difference equationses
dc.titleIntegrability and asymptotic behaviour of a differential-difference matrix equationes
dc.typeinfo:eu-repo/semantics/articlees

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