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  • Research Article
  • Open Access

An Ultradiscrete Matrix Version of the Fourth Painlevé Equation

Advances in Difference Equations20072007:096752

  • Received: 27 February 2007
  • Accepted: 1 May 2007
  • Published:


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.


  • Differential Equation
  • Partial Differential Equation
  • Ordinary Differential Equation
  • Functional Analysis
  • Functional Equation


Authors’ Affiliations

School of Mathematics and Statistics F07, The University of Sydney, Sydney, NSW, 2006, Australia


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© C. M. Field and C. M. Ormerod. 2007

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.