Cellular automata and ultra-discrete Painlevé equations

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

Volumn 226, Issue 1-2, 1997, Pages 53-58

  Grammaticos, B ^a   Ohta, Y ^b   Ramani, A ^c   Takahashi, D ^d   Tamizhmani, K M ^e  

^a UNIVERSITÉ PARIS DESCARTES   (France)

^b HIROSHIMA UNIVERSITY   (Japan)

^c ECOLE POLYTECHNIQUE   (France)

^d RYUKOKU UNIVERSITY   (Japan)

^e PONDICHERRY UNIVERSITY   (India)

Author keywords

[No Author keywords available]

Indexed keywords

INDEPENDENT VARIABLES; INTEGRABILITY; PAINLEVE; SPECIAL SOLUTIONS;

CELLULAR AUTOMATA;

EID: 0039377465     PISSN: 03759601     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0375-9601(96)00934-6     Document Type: Article

References (22)

1. A. Ramani, B. Grammaticos and J. Hietarinta, Phys. Rev. Lett. 67 (1991) 1829.
2. E. Brézin and V.A. Kazakov, Phys. Lett. B 236 (1990) 144.
3. J.A. Shohat, Duke Math. J. 5 (1939) 401.
4. B. Grammaticos and A. Ramani, Retracing the Painlevé-Gambier classification for discrete systems, to appear in Meth. Appl. Anal (1996).
5. [51 B. Grammaticos, A. Ramani and K.M. Tamizhmani, J. Phys. A 27 (1994) 559.
6. T. Tokihiro, D. Takahashi, J. Matsukidaira and J. Satsuma, Phys. Rev. Lett. 76 (1996) 3247.
7. B. Grammaticos, A. Ramani and V. Papageorgiou, Phys. Rev. Lett. 67 (1991) 1825.
8. Y. Pomeau, J. Phys. A 17 (1984) L415.
9. K. Park, K. Steiglitz and W.P. Thurston, Physica D 19 (1986) 423.
10. M.J. Ablowitz J.M. Keiser and L.A. Takhtajan, Phys. Rev. A44 79 (1991) 6909; A.S. Fokas, E. Papadopoulou and Y.G. Saridakis, Physica D41 (1990) 297.
11. M.J. Ablowitz J.M. Keiser and L.A. Takhtajan, Phys. Rev. A44 79 (1991) 6909; A.S. Fokas, E. Papadopoulou and Y.G. Saridakis, Physica D41 (1990) 297.
12. M. Bruschi, P.M. Santini and O. Ragnisco, Phys. Lett. A 169 (1992) 151.
13. A. Bobenko, M. Bordemann, C. Gunn and U. Pinkall, Commun. Math. Phys. 158 (1993) 127.
14. D. Takahashi and J. Satsuma, J. Phys. Soc. Jpn. 59 (1990) 3514.
15. J. Matsukidaira, J. Satsuma, D. Takahashi T. Tokihiro and M. Torii, Toda-type cellular automaton and its N-soliton solution, in preparation.
16. D. Takahashi and J. Matsukidaira, Phys. Lett. A 209 (1995) 184.
17. A. Ramani and B. Grammaticos, Physica A 228 (1996) 160.
18. V.I. Arnold, Bol. Soc. Bras. Mat. 21 (1990) 1.
19. A.P. Veselov, Comm. Math. Phys. 145 (1992) 181.
20. V.I. Gromak and N.A. Lukashevich, The analytic solutions of the Painlevé equations (Universitetskoye Publishers, Minsk, 1990) [in Russian].
21. T. Tokihiro, private communication.
22. A. Ramani, D. Takahashi, B. Grammaticos and Y. Ohta, in preparation.