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Hypergeometric solutions to ultradiscrete Painleve equations

Chris M. Ormerod
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Abstract

We propose new solutions to ultradiscrete Painlevé equations that cannot be derived using the ultradiscretization method. In particular, we show the third ultradiscrete Painelevé equation possesses hypergeometric solutions. We show this by considering a lift of these equations to a non-archimedean valuation field in which we may relax the subtraction free framework of previous explorations of the area. Using several methods, we derive a family of hypergeometric solutions.

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Chris M. Ormerod. 2006-11-24. Hypergeometric solutions to ultradiscrete Painleve equations. https://arxiv.org/abs/nlin/0610048

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