6 Multicomponent q - P IV and its ultradiscrete limit
نویسنده
چکیده
Abstract. We generalize the symmetric fourth q-Painlevé equation (q-PIV) to the noncommutative setting. Considering the symmetric q-PIV to be matrix valued, well-defined multicomponent systems are obtained. The ultradiscrete limit of these systems yields coupled multicomponent ultradiscrete systems that generalize ultradiscrete PIV. The dynamics, and specifically the integrability, of the newly introduced multicomponent ultradiscrete systems is studied.
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