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

SIGMA 7 (2011), 074, 9 pages      arXiv:1107.4416
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

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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