On two-parameter solutions of simultaneous ultradiscrete Painleve II equation with parity variables

TL;DR

This paper introduces a new ultradiscrete Painleve II equation with parity variables, enabling better analysis of two-parameter solutions and their relation to determinant solutions of q-Painleve II.

Contribution

The paper proposes a novel two-parameter ultradiscrete Painleve II equation with parity variables, improving the study of complex solutions compared to previous single-equation approaches.

Findings

Developed a more suitable equation for two-parameter solutions

Analyzed various types of solutions including determinant-type

Established connections with ultradiscrete limits of q-Painleve II solutions

Abstract

We introduce a simultaneous ultradiscrete Painleve II equation with parity variables, which is shown to be more suitable for studying two-parameter solutions than the single second-order ultradiscrete Painleve II equation with parity variables. We investigate several types of two-parameter solutions and the solutions which are related with the ultradiscrete limit of determinant type solutions of q-Painleve II equation.