This article is cited in 5 papers

A Class of Special Solutions for the Ultradiscrete Painlevé II Equation

Shin Isojima, Junkichi Satsuma

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

Abstract: A class of special solutions are constructed in an intuitive way for the ultradiscrete analog of $q$-Painlevé II ($q$-PII) equation. The solutions are classified into four groups depending on the function-type and the system parameter.

Keywords: ultradiscretization; Painlevé equation; Airy equation; $q$-difference equation.

MSC: 34M55; 33E30; 39A13

Received: April 1, 2011; in final form July 14, 2011; Published online July 22, 2011

Language: English

DOI: 10.3842/SIGMA.2011.074

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ArXiv: 1107.4416