Integrability in a discrete world

Chaos, solitons and fractals

Volumn 11, Issue 1, 2000, Pages 7-18

  Grammaticos, B ^a   Ramani, A ^b  

^a UNIVERSITÉ PARIS DESCARTES   (France)

^b CENTRE DE PHYSIQUE THÉORIQUE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

MATHEMATICAL MODELS; ORDINARY DIFFERENTIAL EQUATIONS; POLYNOMIALS;

DISCRETE SYSTEMS; PAINLEVE EQUATIONS; SINGULARITY CONFINEMENT;

INTEGRATION;

EID: 0033928507     PISSN: 09600779     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0960-0779(98)00263-X     Document Type: Article

References (33)

1. A. Einstein, Physics and reality in essay in physics, Philosophical Library, New York, 1950.
2. R.P. Feynman, Intl. J. Theor. Phys. 21 (1982) 467.
3. E. Witten, Reflections on the fate of spacetime, Physics Today, April 1996, p.24.
4. B. Grammaticos, A. Ramani, Integrability, course at the CIMPA 96 Pondicherry school.
5. B. Grammaticos, A. Ramani, V. Papageorgiou, Phys. Rev. Lett. 67 (1991) 1825.
6. A. Ramani, B. Grammaticos, Singularity Confinement, invited talk at the Esterel 94 conference.
7. A. Ramani, B. Grammaticos, J. Satsuma, J. Phys. A 28 (1995) 4655.
8. V. Papageorgiou, B. Grammaticos, A. Ramani, Phys. Lett. A 179 (1993) 111.
9. K. Maruno, K. Kajiwara, S. Nakao, M. Oikawa, Phys. Lett. A 229 (1997) 173.
10. J. Satsuma, A. Ramani, B. Grammaticos, Phys. Lett. A 174 (1993) 387.
11. A. Ramani, B. Grammaticos, J. Satsuma, Phys. Lett. A 169 (1992) 323.
12. B. Grammaticos, A. Ramani, Toda equations and the Painlevé property, invited talk at the Toda 96 symposium.
13. B. Grammaticos, A. Ramani, K.M. Tamizhmani, J. Phys. A 25 (1992) L883.
14. A. Ramani, B. Grammaticos, K.M. Tamizhmani, J. Phys. A 26 (1993) L53.
15. A. Ramani, B. Grammaticos, J. Hietarinta, Phys. Rev. Lett. 67 (1991) 1829.
16. G.R.W. Quispel, J.A.G. Roberts, C.J. Thompson, Physica D 34 (1989) 183.
17. B. Grammaticos, A. Ramani, Meth. Appl. Anal. 4 (1997) 196.
18. A. Ramani, B. Grammaticos, G. Karra, Physica A 181 (1992) 115.
19. B. Grammaticos, A. Ramani, Physica A 223 (1995) 125.
20. B. Grammaticos, F. Nijhoff, A. Ramani, Discrete Painlevé) equations, Course at the Cargèse 96 summer school.
21. A.S. Fokas, B. Grammaticos, A. Ramani, J. Math. An. and Appl. 180 (1993) 342.
22. A.S. Fokas, M.J. Ablowitz, J. Math. Phys. 23 (1982) 2033.
23. F. Nijhoff, J. Satsuma, K. Kajiwara, B. Grammaticos, A. Ramani, Inv. Probl. 12 (1996) 697.
24. A. Ramani, Y. Ohta, J. Satsuma, B. Grammaticos, Comm. Math. Phys. 192 (1998) 67.
25. M. Jimbo, H. Sakai, Lett. Math. Phys. 38 (1996) 145.
26. M. Jimbo, H. Sakai, A. Ramani, B. Grammaticos, Phys. Lett. A 217 (1996) 111.
27. M.D. Kruskal, talk at the Pondicherry CIMPA96 school, unpublished.
28. J. Satsuma, private communication, 1992.
29. M.D. Kruskal, talk at the Montreal 1996 workshop, unpublished.
30. R. Conte, M. Musette, Phys. Lett. A 223 (1996) 439.
31. A.P. Veselov, Comm. Math. Phys. 145 (1992) 181.
32. K. Iwasaki, K. Kimura, S. Shimomura, M. Yoshida, From Gauss to Painlevé, Aspects of Mathematics, 1989.
33. H. Sakai, in preparation.