### 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 language | English |
---|---|

Pages (from-to) | 53-58 |

Number of pages | 6 |

Journal | Physics Letters, Section A: General, Atomic and Solid State Physics |

Volume | 226 |

Issue number | 1-2 |

Publication status | Published - 1997 Feb 10 |

Externally published | Yes |

### Fingerprint

### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*Physics Letters, Section A: General, Atomic and Solid State Physics*,

*226*(1-2), 53-58.

**Cellular automata and ultra-discrete Painlevé equations.** / Grammaticos, B.; Ohta, Y.; Ramani, A.; Takahashi, Daisuke; Tamizhmani, K. M.

Research output: Contribution to journal › Article

*Physics Letters, Section A: General, Atomic and Solid State Physics*, vol. 226, no. 1-2, pp. 53-58.

}

TY - JOUR

T1 - Cellular automata and ultra-discrete Painlevé equations

AU - Grammaticos, B.

AU - Ohta, Y.

AU - Ramani, A.

AU - Takahashi, Daisuke

AU - Tamizhmani, K. M.

PY - 1997/2/10

Y1 - 1997/2/10

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0039377465&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0039377465&partnerID=8YFLogxK

M3 - Article

VL - 226

SP - 53

EP - 58

JO - Physics Letters, Section A: General, Atomic and Solid State Physics

JF - Physics Letters, Section A: General, Atomic and Solid State Physics

SN - 0375-9601

IS - 1-2

ER -