Mikio Murata, “Exact Solutions with Two Parameters for an Ultradiscrete Painlevé Equation of Type <nobr>$A_6^{(1)}$</nobr>”, SIGMA, 2011, Volume 7,059, 15 pp.

This article is cited in 10 papers

Exact Solutions with Two Parameters for an Ultradiscrete Painlevé Equation of Type $A_6^{(1)}$

Mikio Murata

Department of Physics and Mathematics, College of Science and Engineering, Aoyama Gakuin University, 5-10-1 Fuchinobe, Chuo-ku, Sagamihara-shi, Kanagawa, 252-5258 Japan

Abstract: An ultradiscrete system corresponding to the $q$-Painlevé equation of type $A_6^{(1)}$, which is a $q$-difference analogue of the second Painlevé equation, is proposed. Exact solutions with two parameters are constructed for the ultradiscrete system.

Keywords: Painlevé equations; ultradiscrete systems.

MSC: 33E17; 39A12

Received: February 7, 2011; in final form June 11, 2011; Published online June 17, 2011

Language: English

DOI: 10.3842/SIGMA.2011.059