Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-23T18:07:54.255Z Has data issue: false hasContentIssue false
  • English
  • Français

Taming the movable singularities

Published online by Cambridge University Press:  17 February 2009

Jarmo Hietarinta
Jarmo Hietarinta
Affiliation:
Department of Physics, University of Turku, FIN-20014 Turku, Finland; e-mail: [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 have finally obtained for each of the 6 Painlevés an expression of z, w, w′ that behaves as 1/(z − Z0) + O(1) at each kind of movable singular point. This expression is polynomial in w′ (at most quadratic), and rational in w and z. After it is integrated and exponentiated it yields a function that has a simple zero at each of the singular points.

Type
Research Article
Information
The ANZIAM Journal , Volume 44 , Issue 1 , July 2002 , pp. 1 - 9
Copyright
Copyright © Australian Mathematical Society 2002

References

[1]Hietarinta, J., “Painlevé equations in terms of entire functions”, in The Painlevé property: One century later (ed. Conte, R.), (Springer, New York, 1999) 661–686.Google Scholar
[2]Hietarinta, J. and Kruskal, M., “Hirota forms for the six Painlevé equations from singularity analysis”, in Painlevé Transcendent (eds. Levi, D. and Winternitz, P.), (Plenum Press, New York, 1992) 175–185.CrossRefGoogle Scholar
[3]Okamoto, K., “On the τ-function of the Painlevé equations”, Physica D 2 (1980) 525–535.Google Scholar
[4]Painlevé, P., “Sur les équations différentielles du second ordre à points critiques fixes”, C.R. Acad. Sci. Paris 126 (1898) 1697–1700;Google Scholar
[5]Painlevé, P., “Sur les équations différentielles du second ordre à points critiques fixes”, C.R. Acad. Sci. Paris 143 (1906) 1111–1117.Google Scholar
[6]Springael, J., “Direct combinatorial schemes for the application of the Hirota method in soliton theory”, Ph.D. Thesis, Vrije Universiteit Brussels, 1999.Google Scholar