A Hirota bilinear equation for Painlevé transcendents PIV, PII and PI

Hone, Andrew N.W., Zullo, F. (2018) A Hirota bilinear equation for Painlevé transcendents PIV, PII and PI. Random Matrices: Theory and Applications, 7 (4). Article Number 1840001. ISSN 2010-3263. (doi:10.1142/S2010326318400014) (KAR id:70201)

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Official URL: https://doi.org/10.1142/S2010326318400014

Abstract

We present some observations on the tau-function for the fourth Painlev´e equation.

By considering a Hirota bilinear equation of order four for this tau-function,

we describe the general form of the Taylor expansion around an arbitrary movable

zero. The corresponding Taylor series for the tau-functions of the first and

second Painlev´e equations, as well as that for the Weierstrass sigma function,

arise naturally as special cases, by setting certain parameters to zero.

Item Type:	Article
DOI/Identification number:	10.1142/S2010326318400014
Uncontrolled keywords:	Painlevé equation, tau-function, Hirota bilinear form, series expansions
Subjects:	Q Science > QA Mathematics (inc Computing science)
Institutional Unit:	Schools > School of Engineering, Mathematics and Physics > Mathematical Sciences
Former Institutional Unit:	Divisions > Division of Natural Sciences > School of Mathematics Statistics and Actuarial Science Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science
Depositing User:	Andrew Hone
Date Deposited:	20 Nov 2018 10:11 UTC
Last Modified:	20 May 2025 11:39 UTC
Resource URI:	https://kar.kent.ac.uk/id/eprint/70201 (The current URI for this page, for reference purposes)

University of Kent Author Information

Hone, Andrew N.W..

Creator's ORCID:	https://orcid.org/0000-0001-9780-7369
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