Ultradiscrete Painlevé VI with Parity Variables

Abstract

We introduce a ultradiscretization with parity variables of the $q$-difference Painlevé VI system of equations. We show that ultradiscrete limit of Riccati-type solutions of $q$-Painlevé VI satisfies the ultradiscrete Painlevé VI system of equations with the parity variables, which is valid by using the parity variables. We study some solutions of the ultradiscrete Riccati-type equation and those of ultradiscrete Painlevé VI equation.

References in corpus (3)

• Reductions of lattice mKdV to $q$-${\mathrm{P}}_{VI}$
• Exact Solutions with Two Parameters for an Ultradiscrete Painlevé Equation of Type $A_6^{(1)}$
• A Class of Special Solutions for the Ultradiscrete Painlevé II Equation

Cited by in corpus (3)

• On two-parameter solutions of simultaneous ultradiscrete Painleve II equation with parity variables
• Polynomial solutions of $q$-Heun equation and ultradiscrete limit
• Ultradiscrete limit of Bessel function type solutions of the Painlevé III equation