MR1865393 Kenji KAJIWARA, Tetsu MASUDA, Masatoshi NOUMI, Yasuhiro OHTA and Yasuhiko YAMADA Kenji KAJIWARA, Tetsu MASUDA, Masatoshi NOUMI, Yasuhiro OHTA and Yasuhiko YAMADA Determinant Formulas for the Toda and Discrete Toda Equations Funkcialaj Ekvacioj. Serio Internacia 44 2001 291--307 http://fe.math.kobe-u.ac.jp/FE/FullPapers/vol44/fe44-2-6.pdf http://www.ams.org/mathscinet-getitem?mr=MR1865393 44-291 2001 Determinant Formulas for the Toda and Discrete Toda Equations Kenji KAJIWARA, Tetsu MASUDA, Masatoshi NOUMI, Yasuhiro OHTA and Yasuhiko YAMADA Kenji KAJIWARA, Tetsu MASUDA, Masatoshi NOUMI, Yasuhiro OHTA and Yasuhiko YAMADA
1 Kajiwara, K.; Ohta, Y. Determinant Structure of the Rational Solutions for the Painlevé IV Equation J. Phys. A 31 1998 2431-2446 MR1629434
2 Kajiwara, K.; Ohta, Y. Determinant Structure of the Rational solutions for the Painlevé II Equation J. Math. Phys. 37 1996 4693-4704 MR1408115
3 Okamoto, K. Studies on the Painlevé Equations I, Sixth Painlevé equation $P_{VI}$ Annali di Matematica pura ed applicata CXLVI 1987 337-381 MR0916698
4 Okamoto, K. Studies on the Painlevé Equations II, Fifth Painlevé Equation $P_V$ Japan J. Math. 13 1987 47-76 MR0914314
5 Okamoto, K. Studies on the Painlevé Equations III, Second and Fourth Painlevé Equations, $P_{II}$ and $P_{IV}$ Math. Ann. 275 1986 222-254 MR0854008
6 Okamoto, K. Studies on the Painlevé Equations IV, Third Painlevé Equation $P_{III}$ Funkcial. Ekvac. 30 1987 305-332 MR0927186 0927186
7 Kajiwara, K.; Masuda, T. On the Umemura polynomials for the Painlevé III equation Phys. Lett. A260 1999 462-467 MR1722883
8 Kajiwara, K.; Masuda, T. A Generalization of Determinant Formulas for the Solutions of Painlevé II and XXXIV equations J. Phys. A: Math. Gen. 32 1999 3763-3778 MR1694666
9 Leznov, A. N.; Saveliev, M. V. Theory of Group Representations and Integration of Nonlinear Systems $X_{a,z\bar{z}}=\exp(kX)_a$ Physica 3D 1981 62-72 MR0633782
10 Hirota, R.; Ohta, Y.; Satsuma, J. Wronskian Structures of Solutions for Soliton Equations Prog. Theor. Phys. Suppl. 94 1988 59-72 MR0976190
11 Hirota, R.; Ito, M.; Kako, F. Two-Dimensional Toda Lattice Equations Prog. Theor. Phys. Suppl. 94 1988 42-58 MR0976189
12 Hirota, R. Discrete Two-Dimensional Toda Molecule Equation J. Phys. Soc. Jpn. 56 1987 4285-4288 MR0927667
13 Nakamura, A. Bilinear Structure of the Painlevé II Equation and its Solutions for Half Integer Constants J. Phys. Soc. Jpn. 61 1992 3007-3008
14 Noumi, M.; Yamada, Y. Symmetries in the Fourth painleve Equations and Okamoto polynomials Nagoya Math. J. 153 1999 53-86 MR1684551
15 Noumi, M.; Yamada, Y. Umemura polynomials for Painlevé $V$ Equation Phys. Lett. A247 1998 65-69 MR1650509
16 Umemura, H., Special polynomials associated with the Painlevé Equations I, to appear in the proceedings of the Workshop on Painlevé Transcendents, CRM, Montreal, Canada, 1996
17 Noumi, M.; Okada, S.; Okamoto, K.; Umemura, H. Special polynomials associated with the Painlevé Equations II in Integrable Systems and Algebraic Geometry, proceedings of the Taniguchi symposium 1997, World Scientific 1998 349-372 MR1672065