An Ultradiscrete Matrix Version of the Fourth Painlevé Equation

Chris M. Field, Chris M. Ormerod
2007 Advances in Difference Equations  
This paper is concerned with the matrix generalization of ultradiscrete systems. Specifically, we establish a matrix generalization of the ultradiscrete fourth Painlevé equation (ud-P IV ). 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
more » ... discrete systems that generalize ud-P IV . The dynamics, irreducibility, and integrability of the matrix-valued ultradiscrete systems are studied.
doi:10.1155/2007/96752 fatcat:74ypilgd6jdfxl43rkdwlq2hjy