Symmetries and Special Solutions of Reductions of the Lattice Potential KdV Equation

2013/08/31 by Christopher M. Ormerod · 1 citation
Physics and Astronomy · #nlin.SI #msc:39A14 #msc:37K15 #msc:35Q51

paper · pdf · doi:10.3842/sigma.2014.002

published as SIGMA 10 (2014), 002, 19 pages

arxiv created 2014/01/03 · arxiv updated 2014/01/06

Abstract

We identify a periodic reduction of the non-autonomous lattice potential Korteweg-de Vries equation with the additive discrete Painlevé equation with E⁽¹⁾₆ 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.

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