Hostname: page-component-78c5997874-m6dg7 Total loading time: 0 Render date: 2024-11-10T17:16:26.602Z Has data issue: false hasContentIssue false
  • English
  • Français

A determinant formula for a class of rational solutions of Painlevé V equation

Published online by Cambridge University Press:  22 January 2016

Tetsu Masuda ,
Yasuhiro Ohta  and
Kenji Kajiwara
Tetsu Masuda
Affiliation:
Department of Mathematics, Kobe University, Rokko, Kobe, 657-8501, Japan, masuda@math.kobe-u.ac.jp
Yasuhiro Ohta
Affiliation:
Department of Applied Mathematics, Faculty of Engineering, Hiroshima University, 1-4-1 Kagamiyama, Higashi-Hiroshima, 739-8527, Japan, ohta@kurims.kyoto-u.ac.jp
Kenji Kajiwara
Affiliation:
Graduate School of Mathematics, Kyushu University, 6-10-1 Hakozaki, Higashi-ku, Fukuoka, 812-8512, Japan, kaji@math.kyushu-u.ac.jp
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We give an explicit determinant formula for a class of rational solutions of the Painlevé V equation in terms of the universal characters.

Keywords

33E1734M55
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 168 , 2002 , pp. 1 - 25
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2002

References

[1] Jimbo, M. and Miwa, T., Solitons and infinite dimensional Lie algebras, Publ. RIMS. Kyoto Univ., 19 (1983), 943–1001.Google Scholar
[2] Kajiwara, K. and Ohta, Y., Determinant structure of the rational solutions for the Painlevé II equation, J. Math. Phys., 37 (1996), 4693–4704.Google Scholar
[3] Kajiwara, K. and Masuda, T., On the Umemura polynomials for the Painlevé III equation, Phys. Lett., A 260 (1999), 462–467.Google Scholar
[4] Kajiwara, K. and Ohta, Y., Determinant structure of the rational solutions for the Painlevé IV equation, J. Phys. A: Math. Gen., 31 (1998), 2431–2446.Google Scholar
[5] Kitaev, V. A., Law, C. K. and McLeod, J. B., Rational solutions of the fifth Painlevé equation, Differential and Integral Equations, 7 (1994), 967–1000.Google Scholar
[6] Koike, K., On the decomposition of tensor products of the representations of the classical groups: by means of the universal characters, Adv. Math., 74 (1989), 57–86.Google Scholar
[7] Noumi, M., Okada, S., Okamoto, K. and Umemura, H., Special polynomials associated with the Painleve equations II, Proceedings of the Taniguchi Symposium 1997, Integrable Systems and Algebraic Geometry (Saito, M. H., Shimizu, Y. and Ueno, K., eds.), World Scientific, Singapore (1998), pp. 349–372.Google Scholar
[8] Noumi, M. and Yamada, Y., Symmetries in the fourth Painlevé equation and Okamoto polynomials, Nagoya Math. J., 153 (1999), 53–86.Google Scholar
[9] Noumi, M. and Yamada, Y., Umemura polynomials for the Painlevé V equation, Phys. Lett, A247 (1998), 65–69.Google Scholar
[10] Noumi, M. and Yamada, Y., Higher order Painlevé equations of type Af, Funkcial. Ekvac, 41 (1998), 483–503.Google Scholar
[11] Noumi, M. and Yamada, Y., Affine Weyl groups, discrete dynamical systems and Painlevé equations, Commun. Math. Phys, 199 (1998), 281–295.Google Scholar
[12] Okamoto, K., Studies on the Painlevé equations I, sixth Painlevé equation Pvi, Annali di Matematica pura ed applicata, CXLVI (1987), 337–381.Google Scholar
[13] Noumi, M. and Yamada, Y., Studies on the Painlevé equations II, fifth Painlevé equation PV, Japan J. Math., 13 (1987), 47–76.Google Scholar
[14] Noumi, M. and Yamada, Y., Studies on the Painlevé equations III, second and fourth Painlevé equations, P II and PIV , Math. Ann., 275 (1986), 222–254.Google Scholar
[15] Noumi, M. and Yamada, Y., Studies on the Painlevé equations IV, third Painlevé equation PIII , Funkcial. Ekvac, 30 (1987), 305–332.Google Scholar
[16] Taneda, M., Polynomials associated with an algebraic solution of the sixth Painlevé equation, to appear in Jap. J. Math., 27 (2002).Google Scholar
[17] 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).Google Scholar
[18] Noumi, M. and Yamada, Y., Irreducibility of the Painlevé equations-Evolution in the past 100 years, to appear in the Proceedings of the Workshop on “Painlevé Transcendents” (CRM, Montreal, Canada, 1996).Google Scholar
[19] Vorob’ev, P. A., On rational solutions of the second Painlevé equation, Diff. Uravn., 1 (1965), 58–59.Google Scholar
[20] Watanabe, H., Solutions of the fifth Painlevé equation I, Hokkaido Math. J., 24 (1995), 231–267.CrossRefGoogle Scholar
[21] Yamada, Y., Determinant formulas for the generalized Painlevé equations of type A, Nagoya Math. J., 156 (1999), 123–134.Google Scholar