The symplectic Kadomtsev-Petviashvili hierarchy and rational solutions of Painlevé VI

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Equivalence is established between a special class of Painleve VI equations parametrized by a conformal dimension $μ$, time dependent Euler top equations, isomonodromic deformations and three-dimensional Frobenius manifolds. The isomodromic tau function and solutions of the Euler top equations are explicitly constructed in terms of Wronskian solutions of the 2-vector 1-constrained symplectic Kadomtsev-Petviashvili (CKP) hierarchy by means of Grassmannian formulation. These Wronskian solutions give rational solutions of the Painleve VI equation for $μ=1,2,{...} $.
28 pages, lateX

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Exactly Solvable and Integrable Systems, High Energy Physics - Theory, Mathematical Physics, Analysis of PDEs

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http://salesiana.dossiersoluciones.com/handle/123456789/80759

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/nlin/0406038
 http://arxiv.org/abs/nlin/0406038

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arXiv