arXiv subjects

Chris M. Ormerod

Publications and source records attributed to Chris M. Ormerod.

2 recordsLinked to original sources

arXiv2006

An ultradiscrete matrix version of the fourth Painleve equation

We establish a matrix generalization of the ultradiscrete fourth Painlevé equation (ud-PIV). Well-defined multicomponent systems that permit ultradiscretization are obtained using an approach that relies on a group defined by constraints imposed by the requirement of a consistent evolution of the systems. The ultradiscrete limit of these systems yields coupled multicomponent ultradiscrete systems that generalize ud-PIV. The dynamics, irreducibility, and integrability of the matrix valued ultradiscrete systems are studied.

nlin.SI↗

arXiv2006

Hypergeometric solutions to ultradiscrete Painleve equations

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.

nlin.SI↗