# 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). p. 1840001. ISSN 2010-3263. (doi:10.1142/S2010326318400014)

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https://doi.org/10.1142/S2010326318400014

## Abstract

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

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

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 10.1142/S2010326318400014 Painlevé equation, tau-function, Hirota bilinear form, series expansions Q Science > QA Mathematics (inc Computing science) Faculties > Sciences > School of Mathematics Statistics and Actuarial Science Andrew N W Hone 20 Nov 2018 10:11 UTC 29 May 2019 22:05 UTC https://kar.kent.ac.uk/id/eprint/70201 (The current URI for this page, for reference purposes) https://orcid.org/0000-0001-9780-7369