Meromorphy of solutions for a wide class of ordinary differential equations of Painlev\'e type

TL;DR

This paper proves the meromorphy of solutions for a broad class of ODEs related to integrable PDEs, including higher Painlevé analogues, expanding understanding of their solution structures.

Contribution

It establishes the meromorphy of solutions for a wide class of Painlevé-type ODEs derived from integrable PDEs, including higher analogues.

Findings

Solutions are meromorphic for the considered class of equations.

Includes higher analogues of Painlevé equations as examples.

Extends known results to broader classes of integrable ODEs.

Abstract

We prove the meromorphy of solutions for a wide class of ordinary differential equations. These equations are given by invariant manifolds of non-linear partial differential equations integrable by the inverse scattering method. Some higher analogues of the Painlev\' e equations are considered as examples.