Starting from integrable cellular automata we present a novel form of Painlevé equations. These equations are discrete in both the independent variable and the dependent one. We show that they capture the essence of the behavior of the Painlevé equations, organize themselves into a coalescence cascade and possess special solutions. A necessary condition for the integrability of cellular automata is also presented. We conclude with a discussion of the notion of integrability of the cellular automata under examination.
|Number of pages||6|
|Journal||Physics Letters, Section A: General, Atomic and Solid State Physics|
|Publication status||Published - 1997 Feb 10|
ASJC Scopus subject areas
- Physics and Astronomy(all)