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arXiv · 1706.02341

Hirota bilinear equations for Painlevé transcendents

A. N. W. Hone·F. Zullo
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Abstract

We present some observations on the tau-function for the fourth Painlevé 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 Painlevé equations, as well as that for the Weierstrass sigma function, arise naturally as special cases, by setting certain parameters to zero.

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A. N. W. Hone, F. Zullo. 2019-05-04. Hirota bilinear equations for Painlevé transcendents. https://doi.org/10.1142/s2010326318400014

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