The Discrete Painlevé I Hierarchy

dc.creatorCresswell, Clio
dc.creatorJoshi, Nalini
dc.date1997-10-24
dc.date.accessioned2026-07-07T06:17:26Z
dc.date.available2026-07-07T06:17:26Z
dc.descriptionThe discrete Painlevé I equation (dP$\rm_I$) is an integrable difference equation which has the classical first Painlevé equation (P$\rm_I$) as a continuum limit. dP$\rm_I$ is believed to be integrable because it is the discrete isomonodromy condition for an associated (single-valued) linear problem. In this paper, we derive higher-order difference equations as isomonodromy conditions that are associated to the same linear deformation problem. These form a hierarchy that may be compared to hierarchies of integrable ordinary differential equations (ODEs). We strengthen this comparison by continuum limit calculations that lead to equations in the P$\rm_I$ hierarchy. We propose that our difference equations are discrete versions of higher-order Painlevé equations.
dc.description9 pages in LaTeX. To appear in Proceedings of SIDEII, Kent, UK 1996, (eds) P.A.Clarkson and F.Nijhoff
dc.identifierhttps://arxiv.org/abs/solv-int/9710021
dc.identifierhttp://arxiv.org/abs/solv-int/9710021
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/94389
dc.subjectExactly Solvable and Integrable Systems
dc.titleThe Discrete Painlevé I Hierarchy
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