Multicomponent q-P_IV and its ultradiscrete limit

C. M. Field and C. M. Ormerod

Abstract

We generalize the symmetric fourth q-Painleve equation q-P_{VI} to the noncommutative setting. Considering the symmetric q-P_{IV} to be matrix valued, well-defined multicomponent systems are obtained. The ultradiscrete limit of these systems yields coupled multicomponent ultradiscrete systems that generalize ultradiscrete P_{IV}. The dynamics, and specifically the integrability, of the newly introduced multicomponent ultradiscrete systems is studied.

Keywords: Integrable, cellular automata, Painlevé, ultradiscrete.

AMS Subject Classification: Primary 39A13; secondary 33C70, 37J35, 16Y60.