A $q$-analogue of the matrix fifth Painleve system (Mathematical structures of integrable systems, their developments and applications)

Abstract

We consider a degeneration of the q-matrix sixth Painlevé system. As a result, we obtain a system of non-linear q-difference equations, which describes a deformation of a certain “non-Fuchsian” linear q-difference system. We define the spectral type for non-Fuchsian q-difference systems and characterize the associated linear problem in terms of the spectral type. We also consider a continuous limit of the non-linear q-difference system and show that the resulting system of non-linear differential equations coincides with the matrix fifth Painlevé system.