Open Access

An Ultradiscrete Matrix Version of the Fourth Painlevé Equation

Advances in Difference Equations20072007:096752

DOI: 10.1155/2007/96752

Received: 27 February 2007

Accepted: 1 May 2007

Published: 21 June 2007


This paper is concerned with the matrix generalization of ultradiscrete systems. Specifically, we establish a matrix generalization of the ultradiscrete fourth Painlevé equation (ud- ). 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- . The dynamics, irreducibility, and integrability of the matrix-valued ultradiscrete systems are studied.


Authors’ Affiliations

School of Mathematics and Statistics F07, The University of Sydney


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© C. M. Field and C. M. Ormerod. 2007

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