A symmetry reduction technique for higher order Painlev\'e systems

TL;DR

This paper introduces a symmetry reduction method for higher order Painlevé systems using Dirac procedures, providing a systematic way to analyze their Hamiltonian structures.

Contribution

It proposes a set of canonical variables enabling Dirac reduction for Hamiltonian structures of specific higher order Painlevé systems.

Findings

Developed a Dirac-based symmetry reduction framework

Applied to ${A^{(1)}_{2M}}$ and ${A^{(1)}_{2M-1}}$ Painlevé systems

Facilitates analysis of their Hamiltonian structures

Abstract

The symmetry reduction of higher order Painlev\'e systems is formulated in terms of Dirac procedure. A set of canonical variables that admit Dirac reduction procedure is proposed for Hamiltonian structures governing the ${A^{(1)}_{2M}}$ and ${A^{(1)}_{2M-1}}$ Painlev\'e systems for $M=2,3,...$.