This article is cited in 9 papers

Ultradiscrete Painlevé VI with Parity Variables

Kouichi Takemura, Terumitsu Tsutsui

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

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.

Keywords: Painlevé equation; ultradiscrete; numerical solutions.

MSC: 39A13; 34M55; 37B15

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

Language: English

DOI: 10.3842/SIGMA.2013.070

Bibliographic databases:

• 
• 
• 

ArXiv: 1306.4959