Geodesic
Quadratic transformations for the third and fifth Painlevé equations
Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 18, Tome 317 (2004), pp. 105-121 Cet article a éte moissonné depuis la source Math-Net.Ru

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Quadratic transformations for the third and fifth Painlevé equations are constructed via the method of $RS$-transformations. This method can be viewed as a prolongation of the quadratic transformations for the Painlevé equations to the associated linear ODEs, whose isomonodromy deformations are governed by the corresponding Painlevé equations. 
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A. V. Kitaev. Quadratic transformations for the third and fifth Painlevé equations. Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 18, Tome 317 (2004), pp. 105-121. http://geodesic.mathdoc.fr/item/ZNSL_2004_317_a6/

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