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An Ultradiscrete Matrix Version of the Fourth Painlevé Equation

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.

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Correspondence to Chris M. Field.

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Field, C.M., Ormerod, C.M. An Ultradiscrete Matrix Version of the Fourth Painlevé Equation. Adv Differ Equ 2007, 096752 (2007). https://doi.org/10.1155/2007/96752

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Keywords

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