The ultimate discretisation of the Painlevé equations

✍ Scribed by A. Ramani; D. Takahashi; B. Grammaticos; Y. Ohta

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 610 KB
• Volume: 114
• Category: Article
• ISSN: 0167-2789
• DOI: 10.1016/s0167-2789(97)00192-9

✦ Synopsis

We present a systematic way to construct ultra-discrete versions of the Painlev6 equations starting from know discrete forms. These ultra-discrete equations are generalised cellular automata in the sense that the dependent variable takes only integer values. The ultra-discrete Painlev6 equations have the properties characteristic of the continuous and discrete Painlev6"s, namely coalescence cascades, particular solutions and auto-B~icklund relations.