Cellular Automata and Ultra-Discrete Painlevé Equations

英文摘要：

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 organizing themselves into a coalescence cascade and possessing special solutions. A necessary condition for the integrability of cellular automata is also presented.