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


SIGMA 7 (2011), 059, 15 pages      arXiv:1106.3384      http://dx.doi.org/10.3842/SIGMA.2011.059
Contribution to the Special Issue “Relationship of Orthogonal Polynomials and Special Functions with Quantum Groups and Integrable Systems”

Exact Solutions with Two Parameters for an Ultradiscrete Painlevé Equation of Type A6(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

Received February 07, 2011, in final form June 11, 2011; Published online June 17, 2011

Abstract
An ultradiscrete system corresponding to the q-Painlevé equation of type A6(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.

Key words: Painlevé equations; ultradiscrete systems.

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