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An ultradiscrete matrix version of the fourth Painlevé equation. (English) Zbl 1155.39011

Authors’ summary: This paper is concerned with the matrix generalization of ultradiscrete systems. Specifically, we establish a matrix generalization of the ultradiscrete fourth Painlevé equation (ud-\(\text P_{\text{IV}}\)). 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-P\(_{\text{IV}}\). The dynamics, irreducibility, and integrability of the matrix-valued ultradiscrete systems are studied.
Reviewer: D. M. Bors (Iaşi)

MSC:

39A12 Discrete version of topics in analysis
34M55 Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies
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