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An Ultradiscrete Matrix Version of the Fourth Painlevé Equation

Advances in Difference Equations volume 2007, Article number: 096752 (2007) Cite this article

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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Authors and Affiliations

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

    Chris M. Field & Chris M. Ormerod

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  1. Chris M. Field
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  2. Chris M. Ormerod
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Correspondence to Chris M. Field.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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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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