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arXiv · 1509.05248

New Airy-type solutions of the ultradiscrete Painleve II equation with parity variables

Hikaru Igarashi·Shin Isojima·Kouichi Takemura
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Abstract

The q-difference Painleve II equation admits special solutions written in terms of determinant whose entries are the general solution of the q-Airy equation. An ultradiscrete limit of the special solutions is studied by the procedure of ultradiscretization with parity varialbes. Then we obtain new Airy-type solutions of the ultradiscrete Painleve II equation with parity variables, and the solutions have richer structure than the known solutions.

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Hikaru Igarashi, Shin Isojima, Kouichi Takemura. 2015-09-17. New Airy-type solutions of the ultradiscrete Painleve II equation with parity variables. https://arxiv.org/abs/1509.05248

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