@article{SIGMA_2011_7_a29,
author = {Kazuhide Matsuda},
title = {Rational {Solutions} of the {Sasano} {System} of {Type} $A_5^{(2)}$},
journal = {Symmetry, integrability and geometry: methods and applications},
year = {2011},
volume = {7},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SIGMA_2011_7_a29/}
}
Kazuhide Matsuda. Rational Solutions of the Sasano System of Type $A_5^{(2)}$. Symmetry, integrability and geometry: methods and applications, Tome 7 (2011). http://geodesic.mathdoc.fr/item/SIGMA_2011_7_a29/
[1] Airault H., “Rational solutions of Painlevé equation”, Stud. Appl. Math., 61 (1979), 31–53 | MR | Zbl
[2] Bassom A. P., Clarkson P. A., Hicks A. C., “Bäcklund transformations and solution hierarchies for the fourth Painlevé equation”, Stud. Appl. Math., 95 (1995), 1–71 | MR | Zbl
[3] Clarkson P. A., “The third Painlevé equation and associated special polynomial”, J. Phys. A: Math. Gen., 36 (2003), 9507–9532 | DOI | MR | Zbl
[4] Gambier B., “Sur les équations différentielles du second ordre et du premier degré dont l'intégrale générale est a points critique fixes”, Acta Math., 33 (1910), 1–55 | DOI | MR
[5] Gromak V. I., “Algebraic solutions of the third Painlevé equation”, Dokl. Akad. Nauk BSSR, 23 (1979), 499–502 (in Russian) | MR | Zbl
[6] Gromak V. I., “Reducibility of the Painlevé equations”, Differ. Equ., 20 (1983), 1191–1198 | MR
[7] Hone A. N. W., “Coupled Painlevé systems and quartic potentials”, J. Phys. A: Math. Gen., 34 (2001), 2235–2246 | DOI | MR
[8] Kitaev A. V., Law C. K., McLeod J. B., “Rational solutions of the fifth Painlevé equation”, Differential Integral Equations, 7 (1994), 967–1000 | MR | Zbl
[9] Matsuda K., “Rational solutions of the $A_4$ Painlevé equation”, Proc. Japan Acad. Ser. A Math. Sci., 81:5 (2005), 85–88 | DOI | MR | Zbl
[10] Matsuda K., Rational solutions of the $A_5^{(1)}$ Painlevé equation, arXiv: 0708.2960
[11] Mazzoco M., “Rational solutions of the Painlevé VI equation”, J. Phys. A: Math. Gen., 34 (2001), 2281–2294, arXiv: nlin.SI/0007036 | DOI | MR
[12] Mazzoco M., Mo M. Y., “The Hamiltonian structure of the second Painlevé hierarchy,”, Nonlinearity, 20 (2007), 2845–2882, arXiv: nlin.SI/0610066 | DOI | MR
[13] Milne A. E., Clarkson P. A., Bassom A. P., “Bäcklund transformations and solution hierarchies for the third Painlevé equation”, Stud. Appl. Math., 98 (1997), 139–194 | DOI | MR | Zbl
[14] Murata Y., “Rational solutions of the second and the fourth Painlevé equations”, Funkcial. Ekvac., 28 (1985), 1–32 | MR | Zbl
[15] Murata Y., “Classical solutions of the third Painlevé equation”, Nagoya Math. J., 139 (1995), 37–65 | MR | Zbl
[16] Noumi M., Yamada Y., “Higher order Painlevé equations of type $A^{(1)}_l$”, Funkcial. Ekvac., 41 (1998), 483–503, arXiv: math.QA/9808003 | MR | Zbl
[17] Okamoto K., “Studies on the Painlevé equations. III. Second and fourth Painlevé equations, $P\sb{\rm II}$ and $P\sb{\rm IV}$”, Math. Ann., 275 (1986), 221–255 | DOI | MR | Zbl
[18] Okamoto K., “Studies on the Painlevé equations. I. Sixth Painlevé equation $P\sb{\rm VI}$”, Ann. Mat. Pure Appl. (4), 146 (1987), 337–338 | DOI | MR
[19] Okamoto K., “Studies on the Painlevé equations. II. Fifth Painlevé equation $P\sb{\rm V}$”, Japan. J. Math. (N.S.), 13 (1987), 47–76 | MR | Zbl
[20] Okamoto K., “Studies on the Painlevé equations. IV. Third Painlevé equation $P\sb{\rm III}$”, Funkcial. Ekvac., 30 (1987), 305–332 | MR | Zbl
[21] Painlevé P., “Sur les équations différentielles du second ordre et d'ordre supérieur dont l'intégrale générale est uniforme”, Acta Math., 25 (1902), 1–85 | DOI | MR
[22] Sasano Y., “Higher order Painlevé equations of type $D_l^{(1)}$”, RIMS Kokyuroku, 1473:1 (2006), 43–163 | MR
[23] Sasano Y., Symmetries in the system of type $A_5^{(2)}$, arXiv: 0704.2327
[24] Vorob'ev A. P., “On rational solutions of the second Painlevé equation”, Differ. Equ., 1 (1965), 58–59 | MR
[25] Yablonskii A. I., “On rational solutions of the second Painlevé equation”, Vesti AN BSSR, Ser. Fiz.-Tech. Nauk, 1959, no. 3, 30–35 (in Russian)
[26] Yuang W., Li Y., “Rational solutions of Painlevé equations”, Canad. J. Math., 54 (2002), 648–670 | DOI | MR