Reduction of lattice equations to the Painlevé equations: P_{\rm IV} and P_{\rm V}

2017/03/31 by Nobutaka Nakazono · 2 citations
Physics and Astronomy · Mathematics · #nlin.SI #math-ph #math.MP

paper · pdf · doi:10.1063/1.5023252

18 pages, 4 figures

arxiv created 2018/01/06 · arxiv updated 2018/03/14

Abstract

In this paper, we construct a new relation between ABS equations and Painlevé equations. Moreover, using this connection we construct the difference-differential Lax representations of the fourth and fifth Painlevé equations.

Cited by

• On difference-differential Lax pairs and integrals of Painlevé equations in finite characteristic
• Special solutions to five autonomous integrable partial difference equations via the third and sixth Painlevé equations and the Garnier system in two variables