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  • Research Article
  • Open Access

An Ultradiscrete Matrix Version of the Fourth Painlevé Equation

Advances in Difference Equations20072007:096752

https://doi.org/10.1155/2007/96752

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

Abstract

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.

Keywords

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

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Authors’ Affiliations

(1)
School of Mathematics and Statistics F07, The University of Sydney, Sydney, NSW, 2006, Australia

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