Rational Solutions of the Noumi and Yamada System of type $A_5^{(1)}$

TL;DR

This paper classifies all rational solutions of the Noumi and Yamada system of type A5^{(1)}, a generalization of the fifth Painlevé equation, categorizing them into five classes via Bäcklund transformations.

Contribution

It provides a complete classification of rational solutions for the A5^{(1)} Noumi and Yamada system, expanding understanding of its solution structure.

Findings

Rational solutions are classified into five distinct classes.

Bäcklund transformations are used to organize the solutions.

The classification generalizes known solutions of related Painlevé equations.

Abstract

We completely classify all of rational solutions of the Noumi and Yamada system of type $A_5^{(1)}$, which is a generalization of the fifth Painlev\'e equation. The rational solutions are classified to five classes by the B\"acklund transformation group.