Higher order Painlev\'e equations of type $A^{(1)}_l$

TL;DR

This paper introduces a new series of higher order Painlevé equations with affine Weyl group symmetry of type A^{(1)}_l, generalizing classical Painlevé equations P_{IV} and P_{V}.

Contribution

It develops a systematic framework for higher order Painlevé equations based on affine Weyl group symmetry, extending known equations to more complex systems.

Findings

Defines a series of nonlinear equations with affine Weyl symmetry

Generalizes Painlevé IV and V to higher orders

Provides a foundation for further study of integrable systems

Abstract

A series of systems of nonlinear equations with affine Weyl group symmetry of type $A^{(1)}_l$ is studied. This series gives a generalization of Painlev\'e equations $P_{IV}$ and $P_{V}$ to higher orders.