Quadratic Transformations of the Sixth Painlevé Equation
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چکیده
In 1991, one of the authors showed existence of quadratic transformations between Painlevé VI equations with the local monodromy differences (1/2, a, b,±1/2) and (a, a, b, b). In the present paper we give concise forms of these transformation, up to fractional-linear transformations. The transformation is related to better known quadratic transformations (due to Manin and Ramani-Grammaticos-Tamizhmani) via Okamoto transformations. We illustrate the new formulas by deriving an explicit expression for a new algebraic Painlevé VI function. 2000 Mathematics Subject Classification: 34M55, 33E17. Short title: Quadratic transformations of Painlevé VI
منابع مشابه
Quadratic Transformations of the Sixth Painlevé Equation with Application to Algebraic Solutions
In 1991, one of the authors showed the existence of quadratic transformations between the Painlevé VI equations with local monodromy differences (1/2, a, b,±1/2) and (a, a, b, b). In the present paper we give concise forms of these transformations. They are related to the quadratic transformations obtained by Manin and RamaniGrammaticos-Tamizhmani via Okamoto transformations. To avoid cumbersom...
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تاریخ انتشار 1991