Properties of the series solution for Painlevé I

Hone, Andrew N.W. and Ragnisco, Orlando and Zullo, Federico (2013) Properties of the series solution for Painlevé I. Journal of Nonlinear Mathematical Physics, 20 (Supp.1). pp. 85-100. ISSN 1402-9251. (doi:https://doi.org/10.1080/14029251.2013.862436) (Full text available)

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http://dx.doi.org/10.1080/14029251.2013.862436

Abstract

We present some observations on the asymptotic behaviour of the coefficients in the Laurent series expansion of solutions of the first Painlevé equation. For the general solution, explicit recursive formulae for the Taylor expansion of the tau-function around a zero are given, which are natural extensions of analogous formulae for the elliptic sigma function, as given by Weierstrass. Numerical and exact results on the symmetric solution which is singular at the origin are also presented.

Item Type: Article
Subjects: Q Science > QA Mathematics (inc Computing science) > QA299 Analysis, Calculus
Q Science > QA Mathematics (inc Computing science) > QA351 Special functions
Q Science > QA Mathematics (inc Computing science) > QA372 Ordinary differential equations
Divisions: Faculties > Sciences > School of Mathematics Statistics and Actuarial Science
Depositing User: Andrew N W Hone
Date Deposited: 20 Jun 2014 23:34 UTC
Last Modified: 18 Jan 2017 03:43 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/41485 (The current URI for this page, for reference purposes)
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