Symmetries and Special Solutions of Reductions of the Lattice Potential KdV Equation - Ormerod, C.M. (Symmetry, Integrability and Geometry: Methods and Applications, 2014)
We identify a periodic reduction of the non-autonomous lattice potential Korteweg-de Vries equation with the additive discrete Painlevé equation with E₆⁽¹⁾ symmetry. We present a description of a set of symmetries of the reduced equations and their relations to the symmetries of the discrete Painlevé equation. Finally, we exploit the simple symmetric form of the reduced equations to find rational and hypergeometric solutions of this discrete Painlevé equation.