Hostname: page-component-6bf8c574d5-gr6zb Total loading time: 0 Render date: 2025-02-17T14:29:43.225Z Has data issue: false hasContentIssue false
  • English
  • Français

Remarks on the Yablonskii-Vorob’ev polynomials

Published online by Cambridge University Press:  22 January 2016

Makoto Taneda
Makoto Taneda*
Affiliation:
[email protected]
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 study the Yablonskii-Vorob’ev polynomial associated with the second Painlevé equation. To study other special polynomials (Okamoto polynomials, Umemura polynomials) associated with the Painlevé equations, our purely algebraic approach is useful.

Keywords

34M55
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 159 , 2000 , pp. 87 - 111
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2000

References

[1] Date, E., Jimbo, M. and Miwa, T., Soriton no suri, Iwanamikouza, Ouyou sugaku (in Japanese), Iwanami.Google Scholar
[2] Fukutani, S., Okamoto, K. and Umemura, H., Special polynomials associated with the rational solutions of the second and fourth Painlevé equations, Nagoya Math. J., 159 (2000), 179–200.CrossRefGoogle Scholar
[3] Kajiwara, K. and Ohta, Y., Determinant structure of the rational solutions for the Painlevé II equation, J. Math. Phys., 37 (1996), 4693–4704.CrossRefGoogle Scholar
[4] Noumi, M. and Yamada, Y., Symmetries in the fourth Painlevé equation and the Okamoto polynomials, Preprint.CrossRefGoogle Scholar
[5] Noumi, M., Umemura polynomials for the Painlevé V equation, Physics Letters, A 247 (1998), 65–69.CrossRefGoogle Scholar
[6] Okamoto, K., Studies on the Painlevé equations III, Math. Ann., 275 (1986), 221–255.CrossRefGoogle Scholar
[7] Umemura, H., Painlevé equations and classical functions, Sugaku (in Japanese), 47 (1996), 341–359.Google Scholar
[8] Umemura, H., Special Polynomials associated with the Painlevé equation, I, Proceedings of workshop on the Painlevé equations (edited by Winternitz), Montreal, (1996).Google Scholar
[9] Umemura, H. and Watanabe, H., Solutions of the second and fourth Painlevé equations, Nagoya Math J., 151 (1998), 1–24.CrossRefGoogle Scholar