Gordoa, Pilar RPickering, Andrew2024-12-022024-12-022021Journal of Differential Equations 271 (2021) 499–532P.R. Gordoa, A. Pickering, On matrix fourth Painlevé hierarchies, Journal of Differential Equations, Volume 271, 2021, Pages 499-532, ISSN 0022-0396, https://doi.org/10.1016/j.jde.2020.08.0130022-0396https://hdl.handle.net/10115/42251The work of PRG and AP is supported by the Ministry of Economy and Competitiveness of Spain under contract MTM2016-80276-P (AEI/FEDER, EU).We define new matrix fourth Painlevé hierarchies and a new matrix second Painlevé hierarchy. For our matrix fourth Painlevé hierarchies, properties such as auto-Bäcklund transformations, Bäcklund transfor mations and special integrals are derived, and known relations between fourth Painlevé transformations are extended to the matrix ODE hierarchies. The matrix ODE hierarchies presented here are derived as reductions of a new nonisospectral matrix dispersive water wave hierarchy and modifications thereof.engAttribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/matrix Painlevé hierarchiesauto-Bäcklund transformationsinfo:eu-repo/semantics/article10.1016/j.jde.2020.08.013info:eu-repo/semantics/openAccess