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

Symmetry Integrability and Geometry-Methods and Applications

article

Christopher M. Ormerod¹ 

[1] Department of Mathematics, California Institute of Technology

关键词: isometric embedding;    global embedding Minkowski space;    GEMS;    Reissner– Nordstr¨om metric;    charged black hole;   

DOI  :  10.3842/SIGMA.2014.002

来源: National Academy of Science of Ukraine

【 摘 要 】

We identify a periodic reduction of the non-autonomous lattice potential Korteweg-de Vries equation with the additive discrete Painlevé equation with $E_6^{(1)}$ 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.

【 授权许可】

Unknown