On fourth-order nonlinear differential equations with the Painlevé property

Ince, E.L., Ordinary Differential Equations, London, 1926. Translated under the title Obyknovennye differentsial’nye uravneniya, Kharkov, 1939. Ablowitz, M.J. and Clarkson, P.A., Solitons, Nonlinear Evolution Equations and Inverse Scattering, Lect. Notes in Math., Cambridge, 1991, vol. 149. Gromak, V.I. and Lukashevich, N.A., Analiticheskie svoistva reshenii uravnenii Penleve (Analytic Properties of Solutions of Painlevé Equations), Minsk: Universitetskoe, 1990. Iwasaki, K., Kimura, H., Shimomura, S., and Yoshida, M., From Gauss to Painlevé. A Modern Theory of Special Functions, vol. E16 in series: Aspects of Mathematics, Braunschweig: Friedr. Vieweg & Sohn, 1991. Hinkkanen, A. and Laine, I., J. Anal. Math., 1999, vol. 79, pp. 345–377. Gromak, V.I., Laine, I., and Shimomura, S., Painlevé Differential Equations in the Complex Plane, vol. 28 in series: de Gruyter Studies in Mathematics, Berlin: Walter de Gruyter, 2002. Clarkson, P.A., Joshi, N., and Pickering, A., Inverse Problems, 1999, vol. 15, pp. 175–187. Airault, H., Stud. Appl. Math., 1979, vol. 61, pp. 31–53. Kimura, H. and Okamoto, K., J. Math. Pures Appl. (9), 1984, vol. 63, no. 9, pp. 129–146. Okamoto, K., Math. Ann., 1986, vol. 275, pp. 221–255. Okamoto, K., The Painlevé Property, CRM Ser. Math. Phys., New York: Springer, 1999, pp. 735–788. Grammaticos, B., Nijhoff, F.W., and Ramani, A., The Painlevé Property, CRM Ser. Math. Phys., New York: Springer, 1999, pp. 413–517. Flashka, H. and Newell, A.C., Comm. Math. Phys., 1980, vol. 76, pp. 65–116. Jimbo, M., Miwa, T., and Ueno, K., Phys. D, 1981, vol. 2, pp. 306–352. Rogers, C. and Shadwick, R., Bäcklund Transformations and Their Applications, New York: Academic, 1982. Conte, R. and Musette, M., J. Phys. A, 2001, vol. 34, pp. 10507–10522. Ablowitz, M., Ramani, A., and Segur, H., Lett. Nuovo Cimento (2), 1978, vol. 23, pp. 333–338. Kudryashov, N.A., Phys. Lett. A, 1997, vol. 224, pp. 353–360. Manin, Y.I., Amer. Math. Soc. Transl., 1998, vol. 186, no. 6, pp. 131–151. Harnad, J., Tracy, C.A., and Widom, H., NATO Adv. Sci. Inst. Ser. B Phys., 1993, vol. 314, pp. 231–245. Kudryashov, N.A., Teoret. Mat. Fiz., 2000, vol. 122, pp. 72–87. Kudryashov, N.A., ANZIAM J., 2002, vol. 44, pp. 149–160. Kudryashov, N.A., Phys. Lett. A, 2000, vol. 273, pp. 194–202. Cosgrove, C.M., Stud. Appl. Math., 2000, vol. 104, pp. 1–65. Hone, Andrew N.W., Phys. D, 1998, vol. 118, pp. 1–16. Fordy, A.P., Phys. D, 1991, vol. 52, pp. 204–210. Gromak, V.I., Differ. Uravn., 1984, vol. 20, no. 12, pp. 2042–2048.