Hypergeometric Solutions to an Ultradiscrete Painlevé Equation
- 10.1142/S140292511000060XHow to use a DOI?
- Painlevé; discrete; ultradiscrete; hypergeometric; piece-wise linear; integrable; tropical
We show that an ultradiscrete analogue of the third Painlevé equation admits discrete Riccati type solutions. We derive these solutions by considering a framework in which the ultradiscretization process arises as a restriction of a non-archimedean valuation over a field. Using this framework we may relax the conditions one requires to apply the ultradiscretization process. We derive a family of transcendental solutions that appear as the non-archimedean field valuation of hypergeometric functions.
- © 2010 The Authors. Published by Atlantis Press and Taylor & Francis
- Open Access
- This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).
Cite this article
TY - JOUR AU - Christopher M. Ormerod PY - 2021 DA - 2021/01/07 TI - Hypergeometric Solutions to an Ultradiscrete Painlevé Equation JO - Journal of Nonlinear Mathematical Physics SP - 87 EP - 102 VL - 17 IS - 1 SN - 1776-0852 UR - https://doi.org/10.1142/S140292511000060X DO - 10.1142/S140292511000060X ID - Ormerod2021 ER -