Hypergeometric solutions to ultradiscrete Painleve equations
Exactly Solvable and Integrable Systems
2007-05-23 v2
Abstract
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.
Cite
@article{arxiv.nlin/0610048,
title = {Hypergeometric solutions to ultradiscrete Painleve equations},
author = {Chris M. Ormerod},
journal= {arXiv preprint arXiv:nlin/0610048},
year = {2007}
}
Comments
11 pages, 2 figures, addition of a short proof