The Discrete Painlevé I Hierarchy
| dc.creator | Cresswell, Clio | |
| dc.creator | Joshi, Nalini | |
| dc.date | 1997-10-24 | |
| dc.date.accessioned | 2026-07-07T06:17:26Z | |
| dc.date.available | 2026-07-07T06:17:26Z | |
| dc.description | The 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.description | 9 pages in LaTeX. To appear in Proceedings of SIDEII, Kent, UK 1996, (eds) P.A.Clarkson and F.Nijhoff | |
| dc.identifier | https://arxiv.org/abs/solv-int/9710021 | |
| dc.identifier | http://arxiv.org/abs/solv-int/9710021 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/94389 | |
| dc.subject | Exactly Solvable and Integrable Systems | |
| dc.title | The Discrete Painlevé I Hierarchy | |
| dc.type | text |