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The paper is devoted to non-Schlesinger isomonodromic deformations forresonant Fuchsian systems. There are very few explicit examples of suchdeformations in the literature. In this paper we construct a new example of thenon-Schlesinger isomonodromic deformation for a resonant Fuchsian system oforder 5 by using middle convolution for a resonant Fuchsian system of order 2.Moreover, it is known that middle convolution is an operation that preservesSchlesinger's deformation equations for non-resonant Fuchsian systems. In thispaper we show that Bolibruch's non-Schlesinger deformations of resonantFuchsian systems are, in general, not preserved by middle convolution.

Non-Schlesinger Isomonodromic Deformations of Fuchsian Systems and Middle Convolution