TY - JOUR

T1 - Cellular automata and ultra-discrete Painlevé equations

AU - Grammaticos, B.

AU - Ohta, Y.

AU - Ramani, A.

AU - Takahashi, D.

AU - Tamizhmani, K. M.

N1 - Funding Information:
The authorsa re grateful to J. Satsumaa nd T. Toki-hiro for stimulating discussions. B. Grammaticos and K.M. Tamizhmani wish to acknowledget he financial support of the CEFIPRA (under contract 1201-I ) , which has made the presentc ollaboration possible. Y. Ohta acknowledgest he financial supporto f the Japan Ministry of Education through the Foreign Study Program. B. Grammaticos acknowledges an interesting discussion with A. Magnus who introducedh im to the prehistoryo f discreteP ainleve equations.

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.

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U2 - 10.1016/S0375-9601(96)00934-6

DO - 10.1016/S0375-9601(96)00934-6

M3 - Article

AN - SCOPUS:0039377465

SN - 0375-9601

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

IS - 1-2

ER -