New contiguity relation of the sixth Painlevé equation from a truncation

Abstract

For the master Painlevé equation P6(u), we define a consistent method, adapted from the Weiss truncation for partial differential equations, which allows us to obtain the first degree birational transformation of Okamoto. Two new features are implemented to achieve this result. The first one is the homography between the derivative of the solution $u$ and a Riccati pseudopotential. The second one is an improvement of a conjecture by Fokas and Ablowitz on the structure of this birational transformation. We then build the contiguity relation of P6, which yields one new second order nonautonomous discrete equation.

arXiv commentLaTex 2e. To appear, Physica D

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Cited by in corpus (4)

• First degree birational transformations of the Painlevé equations and their contiguity relations
• Geometry of the Ising persistence problem and the universal Bonnet-Manin Painlevé VI distribution
• Quadratic Transformations of the Sixth Painleve' Equation with Application to Algebraic Solutions
• A truncation for obtaining all the first degree birational transformations of the Painlevé transcendents