Gordoa, Pilar RPickering, Andrew2024-12-022024-12-022019-04P.R. Gordoa, A. Pickering, Bäcklund transformations for a new extended Painlevé hierarchy, Communications in Nonlinear Science and Numerical Simulation, Volume 69, 2019, Pages 78-97, ISSN 1007-5704, https://doi.org/10.1016/j.cnsns.2018.09.0141007-5704https://hdl.handle.net/10115/42240This work is supported by the Ministry of Economy and Competitiveness of Spain under contract MTM2016-80276-P (AEI / FEDER, EU). We also gratefully acknowledge financial support from Universidad Rey Juan Carlos - Banco de Santander (Excellence group QUINANOAP, Convocatoria de ayudas a la Actividad de Grupos de Excelencia Investigadora).In a recent paper we introduced an extended second Painlevé hierarchy and studied its properties. The approach developed in order to derive these results is widely applicable. Here we use it to obtain a second example of an extended Painlevé hierarchy. We also give results on Bäcklund transformations, auto-Bäcklund transformations and other properties of this and related hierarchies of ordinary differential equations, as well as on the nesting of equations whereby we obtain relations between systems of different orders but of the same form.engAttribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/Extended Painlevé hierarchyBäcklund transformationsinfo:eu-repo/semantics/article10.1016/j.cnsns.2018.09.014info:eu-repo/semantics/embargoedAccess