REFERENCES
[1] M. J. Ablowitz and P. A. Clarkson, Solitons, Nonlinear Evolution Equations and Inverse Scattering,
Cambridge University Press, 1991.
[2] M. J. Ablowitz, A. Ramani and H. Segur, A connection between nonlinear evolution equations
and ordinary differential equations of P-type II, J. Math. Phys., 21 (1980), no. 5, 1006–1015.
[3] C. J. Earle and R. S. Hamilton, A fixed point theorem for holomorphic mappings, In: Global
Analysis Proceedings Symposium Pure Mathematics, XVI, Berkeley, California, 1968, 61–65,
American Mathematical Society, Providence, R.I., 1970
[4] A. S. Fokas U. Mugan and X. Zhou, On the solvability of Painlev´e I, III and V, Inverse
Problems, 8 (1992), 757–785.
[5] A. S. Fokas and X. Zhou, On the solvability of Painlev´e II and IV, Comm. Math. Phys., 144 (1992), 601–622.
[6] E. Hille, Ordinary Differential Equations in the Complex Domain, Pure and Applied Mathematics,
A. Wiley-Interscience Series of Texts, Monographs and Tracts, 1976.
[7] A. Hinkkanen and I. Laine, Solutions of the first and second Painlev´e equations are meromorphic,
J. Analyse Math., 79 (1999), 345–377.
[8] E. K. Ifantis, An existence theory for functional-differential equations and functionaldifferential
systems, J. Diff. Equat., 29 (1978), no. 1, 86–104.
[9] E. K. Ifantis, Analytic solutions for nonlinear differential equations, J. Math. Anal. Appl., 124
(1987), no. 2, 339–380.
[10] E. K. Ifantis, Global analytic solutions of the radial nonlinear wave equation, J. Math. Anal.
Appl., 124 (1987), no. 2, 381–410.
[11] A. R. Its, Connection formulae for the Painlev´e transcendents, In: The Stokes Phenomenon
and Hilbert’s 16th Problem (Groningen, 1995), World Sci. Publishing, River Edge, NJ (1996).
[12] A. R. Its and V. Yu. Novokshenov, The Isomonodromic Deformation Method in the Theory of
Painlev´e Equations, Lecture Notes in Mathematics, 1191, Springer-Verlag, Berlin-New York 1986.
[13] N. A. Lukaˇseviˇc, The solutions of Painlev´e’s fifth equation, Differencial’nye Uravnenija, 4
(1968), 1413–1420, In Russian.
[14] B. M. McCoy, C. A. Tracy and T. T. Wu, Painlev´e functions of the third kind, J. Math. Phys.,
18 (1977), no. 5, 1058–1092.
[15] Y. Murata, Rational solutions of the second and fourth Painlev´e equations, Funkc. Ekvac., 28
(1985), 1–32.
[16] P. Painlev´e, Lecons sur la Th´eorie Analytique des Equations Diff´erentielles, Profes´ees ´ a`, Stockholm
1895, Hermann, Paris, 1897.
[17] R. R. Rosales, The similarity solution for the Kortegew-de-Vries equation and the related
Painlev´e transcedent, Proc. R. Soc. Lond. A, 361 (1978), 265–275.
[18] P. D. Siafarikas, A singular functional-differential equation, Inter. J. Math. & Math. Sci., 5
(1982), no. 3, 497–501.
[19] P. D. Siafarikas, Conditions for analytic solutions of a singular differential equation, Appl.
Anal., 17 (1983), 1–12.
[20] P. D. Siafarikas, On the number of analytic solutions of a singular differential system, Complex
Var., 4 (1984), 49–56.
[21] N. Steinmetz, On Painlev´e’s equations I, II and IV, J. Analyse Math., 82 (2000), 363–377.