Auxiliary differential polynomials for the first Painlevé hierarchy

Abstract

This article concerns with the first Painleve hierarchy, i.e. the $2n$-th order analogues of the first Painleve equation. Several higher order analogues of the first Painleve equation are proposed by several authors however, we investigate one derived from the KdV hierarchy by studying singularity manifold. We give the auxiliary differential polynomials of the first Painleve hierarchy.