Rational solutions of the Noumi and Yamada system of type $A_4^{(1)}$

TL;DR

This paper classifies all rational solutions of the Noumi and Yamada system of type A_4^{(1)}, a generalization of the fourth Painlevé equation, using Bäcklund transformations to categorize three solution types.

Contribution

It provides a complete classification of rational solutions for the A_4^{(1)} Noumi-Yamada system, expanding understanding of its solution structure.

Findings

Rational solutions are classified into three types.

Bäcklund transformations are used to categorize solutions.

Complete classification of rational solutions achieved.

Abstract

In this paper, we completely classify the raional solutions of the Noumi and Yamada system of type A_4^{(1)}, which is a generalization of the forth Painlev\'e equation. The rational solutions are classified to three types by the B\"acklund transformation group.