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

**Ormerod, C ***(La Trobe University)*

Friday 12 July 2013, 09:30-10:00

Seminar Room 1, Newton Institute

#### Abstract

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 Painlevé equation admitting an affine Weyl group of type $E_6^{(1)}$ as a group of Bäcklund transformations. We use the reduced equations to obtain a family of explicitrational and hypergeometricsolutions of this discrete Painlevé equation.

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