Quadratic Transformations of the Sixth Painleve Equation with Application to Algebraic SolutionsReport as inadecuate



 Quadratic Transformations of the Sixth Painleve Equation with Application to Algebraic Solutions


Quadratic Transformations of the Sixth Painleve Equation with Application to Algebraic Solutions - Download this document for free, or read online. Document in PDF available to download.

Download or read this book online for free in PDF: Quadratic Transformations of the Sixth Painleve Equation with Application to Algebraic Solutions
In 1991, one of the authors showed the existence of quadratic transformations between the Painleve VI equations with local monodromy differences $1-2,a,b,\pm 1-2$ and $a,a,b,b$. In the present paper we give concise forms of these transformations. %, up to fractional-linear transformations. They are related to the %better known quadratic transformations obtained by Manin and Ramani-Grammaticos-Tamizhmani via Okamoto transformations. To avoid cumbersome expressions with differentiation, we use contiguous relations instead of the Okamoto transformations. The 1991 transformation is particularly important as it can be realized as a quadratic-pull back transformation of isomonodromic Fuchsian equations. The new formulas are illustrated by derivation of explicit expressions for several complicated algebraic Painleve VI functions.



Author: Raimundas Vidunas; Alexander V. Kitaev

Source: https://archive.org/







Related documents