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SIGMA 7 (2011), 074, 9 pages arXiv:1107.4416
https://doi.org/10.3842/SIGMA.2011.074
Contribution to the Proceedings of the Conference “Integrable Systems and Geometry”
A Class of Special Solutions for the Ultradiscrete Painlevé II Equation
Shin Isojima and Junkichi Satsuma
Department of Physics and Mathematics, Aoyama Gakuin University, 5-10-1 Fuchinobe, Chuo-ku, Sagamihara-shi, Kanagawa, 252-5258, Japan
Received April 01, 2011, in final form July 14, 2011; Published online July 22, 2011
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.
Key words:
ultradiscretization; Painlevé equation; Airy equation; q-difference equation.
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