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Special solutions of the additive discrete Painlev equation with $E_6^{(1)}$ symmetry

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Discrete Integrable Systems

We consider a reduction of the lattice potential Korteweg-de Vries equation. Using a parameterization of the Lax pair of Arinkin and Borodin, we identify the reduction as the additive discrete Painlev equation admitting an affine Weyl group of type $E_6^{(1)}$ as a group of Bcklund transformations. We use the reduced equations to obtain a family of explicitrational and hypergeometricsolutions of this discrete Painlev equation.

This talk is part of the Isaac Newton Institute Seminar Series series.

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