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arXiv · 0804.0785

Solutions of the Painleve VI Equation from Reduction of Integrable Hierarchy in a Grassmannian Approach

H. Aratyn·J. van de Leur
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Abstract

We present an explicit method to perform similarity reduction of a Riemann-Hilbert factorization problem for a homogeneous GL (N, C) loop group and use our results to find solutions to the Painleve VI equation for N=3. The tau function of the reduced hierarchy is shown to satisfy the sigma-form of the Painleve VI equation. A class of tau functions of the reduced integrable hierarchy is constructed by means of a Grassmannian formulation. These solutions provide rational solutions of the Painleve VI equation.

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H. Aratyn, J. van de Leur. 2008-04-04. Solutions of the Painleve VI Equation from Reduction of Integrable Hierarchy in a Grassmannian Approach. https://doi.org/10.1093/imrn%2Frnn080

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