Exact Solutions with Two Parameters for an Ultradiscrete Painlev\'e Equation of Type $A_6^{(1)}$

TL;DR

This paper constructs exact two-parameter solutions for an ultradiscrete system related to the $A_6^{(1)}$ type $q$-Painlevé equation, advancing understanding of discrete integrable systems.

Contribution

It introduces exact solutions with two parameters for the ultradiscrete $A_6^{(1)}$ Painlevé system, a novel contribution to ultradiscrete integrable equations.

Findings

Exact two-parameter solutions are constructed.

The ultradiscrete system is derived from the $q$-Painlevé $A_6^{(1)}$ equation.

The solutions provide insight into the structure of ultradiscrete Painlevé equations.

Abstract

An ultradiscrete system corresponding to the $q$-Painlev\'e equation of type $A_6^{(1)}$, which is a $q$-difference analogue of the second Painlev\'e equation, is proposed. Exact solutions with two parameters are constructed for the ultradiscrete system.