A reduction of the ultradiscrete modified KdV equation and its finite order solutions

Abstract In this paper we will perform a reduction on the ultradiscrete modified Korteweg–De Vries equation. We will then describe the form of the solutions of the reduction in detail. We will also show that with certain parameter values the equation acquired from the reduction possesses only finite order solutions while with other parameter values the equation possesses infinite order solutions. Finally, we will pose a conjecture about the ultradiscrete Painlevé I equation.