Hypergeometric solutions to ultradiscrete Painleve equations

Details Hypergeometric solutions to ultradiscrete Painleve equations Hypergeometric solutions to ultradiscrete Painleve equations

2006-10-20

arxiv.org/abs/nlin/0610048v2

Nonlinear Sciences

Exactly Solvable and Integrable Systems

11 pages, 2 figures, addition of a short proof

Scientific paper

We propose new solutions to ultradiscrete Painlev\'e equations that cannot be derived using the ultradiscretization method. In particular, we show the third ultradiscrete Painelev\'e 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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