1. Hypergeometric solutions to ultradiscrete Painleve equations
- Author
-
Ormerod, Chris M.
- Subjects
Nonlinear Sciences::Exactly Solvable and Integrable Systems ,Nonlinear Sciences - Exactly Solvable and Integrable Systems ,FOS: Physical sciences ,Exactly Solvable and Integrable Systems (nlin.SI) ,Nonlinear Sciences::Cellular Automata and Lattice Gases - 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., Comment: 11 pages, 2 figures, addition of a short proof
- Published
- 2006