Cellular automata and ultra-discrete Painlevé equations

B. Grammaticos, Y. Ohta, A. Ramani, Daisuke Takahashi, K. M. Tamizhmani

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Abstract

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.

Original languageEnglish
Pages (from-to)53-58
Number of pages6
JournalPhysics Letters, Section A: General, Atomic and Solid State Physics
Volume226
Issue number1-2
Publication statusPublished - 1997 Feb 10
Externally publishedYes

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ASJC Scopus subject areas

  • Physics and Astronomy(all)

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