A Class of Special Solutions for the Ultradiscrete Painlev\'e II Equation

TL;DR

This paper constructs and classifies special solutions for the ultradiscrete Painlevé II equation, providing insights into its structure and solution types.

Contribution

It introduces a novel method for constructing special solutions and classifies them into four distinct groups based on function type and parameters.

Findings

Solutions classified into four groups.

Constructed solutions using an intuitive approach.

Enhanced understanding of ultradiscrete Painlevé II solutions.

Abstract

A class of special solutions are constructed in an intuitive way for the ultradiscrete analog of $q$-Painlev\'e II ($q$-PII) equation. The solutions are classified into four groups depending on the function-type and the system parameter.