We consider deformations of a differential system with Poincare’ rank 1 at
    infinity and Fuchsian singularity at zero along a stratum of a coalescence
    locus. We give necessary and sufficient conditions for the deformation to be
    strongly isomonodromic, both as an explicit Pfaffian system (integrable
    deformation) and as a non linear system of PDEs on the residue matrix A at the
    Fuchsian singularity. This construction is complementary to that of [13]. For
    the specific system here considered, the results generalize those of [26], by
    giving up the generic conditions, and those of [3], by giving up the Lidskii
    generic assumption. The importance of the case here considered originates form
    its applications in the study of strata of Dubrovin-Frobenius manifolds and

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