Note on the Painlev\'e V tau-functions
Yu.P. Bibilo, R.R. Gontsov
TL;DR
This paper investigates properties of tau-functions related to the fifth Painlevé equation, providing an elementary proof of Miwa's formula for their logarithmic differential, enhancing understanding of isomonodromic deformations.
Contribution
It offers a new elementary proof of Miwa's formula for tau-functions associated with Painlevé V, clarifying their differential properties.
Findings
Elementary proof of Miwa's formula established
Enhanced understanding of tau-function properties
Contributions to isomonodromic deformation theory
Abstract
We study some properties of tau-functions of an isomonodromic deformation leading to the fifth Painlev\'e equation. In particular, here is given an elementary proof of Miwa's formula for the logarithmic differential of a tau-function.
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Taxonomy
TopicsNonlinear Waves and Solitons · Mathematical functions and polynomials · Analytic and geometric function theory