Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)


SIGMA 9 (2013), 070, 12 pages      arXiv:1306.4959      http://dx.doi.org/10.3842/SIGMA.2013.070

Ultradiscrete Painlevé VI with Parity Variables

Kouichi Takemura and Terumitsu Tsutsui
Department of Mathematics, Faculty of Science and Technology, Chuo University, 1-13-27 Kasuga, Bunkyo-ku Tokyo 112-8551, Japan

Received July 15, 2013, in final form November 11, 2013; Published online November 19, 2013

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.

Key words: Painlevé equation; ultradiscrete; numerical solutions.

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