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An ultradiscrete matrix version of the fourth Painleve equation

Chris M. Field·Chris M. Ormerod
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Abstract

We establish a matrix generalization of the ultradiscrete fourth Painlevé equation (ud-PIV). 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-PIV. The dynamics, irreducibility, and integrability of the matrix valued ultradiscrete systems are studied.

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Chris M. Field, Chris M. Ormerod. 2006-12-06. An ultradiscrete matrix version of the fourth Painleve equation. https://arxiv.org/abs/nlin/0610041

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