dorsal/arxiv
View SchemaCellular Automata and Ultra-Discrete Painlev\'e Equations
| Authors | B. Grammaticos, Y. Ohta, A. Ramani, D. Takahashi, K. M. Tamizhmani |
|---|---|
| Categories | |
| ArXiv ID | solv-int/9603003 |
| URL | https://arxiv.org/abs/solv-int/9603003 |
| DOI | 10.1016/S0375-9601(96)00934-6 |
Abstract
Starting from integrable cellular automata we present a novel form of Painlev\'e 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 Painlev\'e equations organizing themselves into a coalescence cascade and possessing special solutions. A necessary condition for the integrability of cellular automata is also presented.
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"abstract": "Starting from integrable cellular automata we present a novel form of\nPainlev\\\u0027e equations. These equations are discrete in both the independent\nvariable and the dependent one. We show that they capture the essence of the\nbehavior of the Painlev\\\u0027e equations organizing themselves into a coalescence\ncascade and possessing special solutions. A necessary condition for the\nintegrability of cellular automata is also presented.",
"arxiv_id": "solv-int/9603003",
"authors": [
"B. Grammaticos",
"Y. Ohta",
"A. Ramani",
"D. Takahashi",
"K. M. Tamizhmani"
],
"categories": [
"solv-int",
"nlin.SI"
],
"doi": "10.1016/S0375-9601(96)00934-6",
"title": "Cellular Automata and Ultra-Discrete Painlev\\\u0027e Equations",
"url": "https://arxiv.org/abs/solv-int/9603003"
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