References
- Clarkson , P. A. , Joshi , N. and Pickering , A. 1999 . Bäcklund transformations for the second Painlevé hierarchy: a modified truncation approach . Inverse Problems , 15 : 175 – 187 .
- Gordoa , P. , Joshi , N. and Pickering , A. 1999 . Mappings preserving locations of movable poles: a new extension of the truncation method to ordinary differential equations . Nonlinearity , 12 : 955 – 968 .
- Conte R. Musette M. New contiguity relation of the sixth Painlevé equation from a truncation, 13 pages, preprint S2001/009, submitted (2001)
- Conte R. Musette M. First degree birational transformations of the Painlevé equations and their contiguity relations, to appear in J. Phys. A (2001), nlin.SI/0110028, Special issue SIDE IV Proceedings, Tokyo, 27 November - 1 December 2000
- Conte R. Sur les transformations de Schlesinger de la sixième équation de Painlevé, C. R. Acad. Sc. Paris 332 (2001) 501–504. math.CA/0103165
- Okamoto , K. 1987 . Studies on the Painlevé equations, I, Sixth Painlevé equation . Ann. Mat. Pura Appl. , 146 : 337 – 381 .
- Weiss , J. , Tabor , M. and Carnevale , G. 1983 . The Painlevé property for partial differential equations . J. Math. Phys. , 24 : 522 – 526 .
- Musette , M. 1999 . “ Painlevé analysis for nonlinear partial differential equations ” . In The Painlevé property, one century later , Edited by: Conte , R. 517 – 572 . New York : Springer . CRM series in mathematical physics
- Conte R. Exact solutions of nonlinear partial differential equations by singularity analysis, Direct and inverse methods in nonlinear evolution equations, 83 pages, ed. A. Greco (Springer, Berlin, 2001). nlin-SI/0009024. CIME school, Cetraro, 5–12 September 1999
- P. Painlevé Leçons sur la théorie analytique des équations différentielles (Leçons de Stock-holm, 1895) (Hermann, Paris, 1897). Reprinted, Oeuvres de Paul Painlevé, vol. I (Éditions du CNRS, Paris, 1973)
- Fuchs , R. 1905 . Sur quelques équations différentielles linéaires du second ordre . C. R. Acad. Sc. Paris , 141 : 555 – 558 .
- Gibbon , J. D. , Newell , A. C. , Tabor , M. and Zeng , Y.-b . 1988 . Lax pairs, Bäcklund transformations and special solutions for ordinary differential equations . Nonlinearity , 1 : 481 – 490 .
- Gromak , V. I. 1976 . Solutions of Painlevé’s fifth problem . Differentsial’nye Uravneniya , 12 : 740 – 746 . [English: Diff. equ. 12 (1976) 519–521]
- Okamoto , K. 1987 . Studies on the Painlevé equations, II, Fifth Painlevé equation . Japan. J. Math. , 13 : 47 – 76 .
- Okamoto , K. 1986 . Isomonodromic deformation and Painlevé equations, and the Garnier system . J. Fac. Sci. Univ. Tokyo, Sect. IA , 33 : 575 – 618 .
- Gordoa , P. , Joshi , N. and Pickering , A. 2001 . Mappings preserving locations of movable poles: II. The third and fifth Painlevé equations . Nonlinearity , 14 : 567 – 582 .