Ultradiscrete Painlev\'e VI with Parity Variables
Classical Analysis and ODEs
2013-11-20 v2 Mathematical Physics
math.MP
Quantum Algebra
Abstract
We introduce a ultradiscretization with parity variables of the -difference Painlev\'e VI system of equations. We show that ultradiscrete limit of Riccati-type solutions of -Painlev\'e VI satisfies the ultradiscrete Painlev\'e 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 Painlev\'e VI equation.
Cite
@article{arxiv.1306.4959,
title = {Ultradiscrete Painlev\'e VI with Parity Variables},
author = {Kouichi Takemura and Terumitsu Tsutsui},
journal= {arXiv preprint arXiv:1306.4959},
year = {2013}
}