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À propos de : Solutions of the Painlevé VI Equation from Reduction of Integrable Hierarchy in a Grassmannian Approach        

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  • Solutions of the Painlevé VI Equation from Reduction of Integrable Hierarchy in a Grassmannian Approach
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  • We present an explicit method to perform similarity reduction of a n-Hilbert factorization problem for a homogeneous loop group and use our results to find solutions to the Painlevé VI equation for N = 3. The tau function of the reduced hierarchy is shown to satisfy the σ-form of the Painlevé 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 Painlevé VI equation.
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  • rnn080
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  • H. Aratyn and J. van de Leur
  • Solutions of the Painlevé VI Equation
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