A $q$-analogue of the matrix fifth Painlev\'e system

Hiroshi Kawakami

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arXiv · 2301.12837

A $q$-analogue of the matrix fifth Painlev\'e system

Hiroshi Kawakami

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Abstract

We consider a degeneration of the $q$-matrix sixth Painlev\'e 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 Painlev\'e system.

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Hiroshi Kawakami. 2023-01-30. A $q$-analogue of the matrix fifth Painlev\'e system. https://arxiv.org/abs/2301.12837

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