We present some observations on the tau-function for the fourth Painle v´e equation. By considering a Hirota bilinear equation of order four for this tau-function, we describ e the general form of the Taylor expansion around an arbitrary movable ze ro. The corresp onding Taylor series for the tau-functions of the first and second Painlev´e equations, as we ll as that for the Weierstrass sigma function, arise naturally as sp ecial cases, by setting certain parameters to zero.
A Hirota bilinear equation for Painlevé transcendents PIV, PII and PI.
zullo, federico
2018-01-01
Abstract
We present some observations on the tau-function for the fourth Painle v´e equation. By considering a Hirota bilinear equation of order four for this tau-function, we describ e the general form of the Taylor expansion around an arbitrary movable ze ro. The corresp onding Taylor series for the tau-functions of the first and second Painlev´e equations, as we ll as that for the Weierstrass sigma function, arise naturally as sp ecial cases, by setting certain parameters to zero.File in questo prodotto:
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