We consider a Pfaffian system expressing isomonodromy of an irregular system of Okubo type, depending on complex deformation parameters \(u=(u_1,\ldots ,u_n)\), which are eigenvalues of the leading matrix at the irregular singularity. At the same time, we consider a Pfaffian system of non-normalized Schlesinger-type expressing isomonodromy of a Fuchsian system, whose poles are the deformation parameters \(u_1,\ldots ,u_n\). The parameters vary in a polydisc containing a coalescence locus for the eigenvalues of the leading matrix of the irregular system, corresponding to confluence of the Fuchsian singularities. We construct isomonodromic selected and singular vector solutions of the Fuchsian Pfaffian system together with their isomonodromic connection coefficients, so extending a result of Balser et al. (I SIAM J Math Anal 12(5): 691–721, 1981) and Guzzetti (Funkcial Ekvac 59(3): 383–433, 2016) to the isomonodromic case, including confluence of singularities. Then, we introduce an isomonodromic Laplace transform of the selected and singular vector solutions, allowing to obtain isomonodromic fundamental solutions for the irregular system, and their Stokes matrices expressed in terms of connection coefficients. These facts, in addition to extending (Balser et al. in I SIAM J Math Anal 12(5): 691–721, 1981; Guzzetti in Funkcial Ekvac 59(3): 383–433, 2016) to the isomonodromic case (with coalescences/confluences), allow to prove by means of Laplace transform the main result of Cotti et al. (Duke Math J arXiv:1706.04808, 2017), namely the analytic theory of non-generic isomonodromic deformations of the irregular system with coalescing eigenvalues.

我们考虑表达大久保型不规则系统的等单性的 Pfaffian 系统，这取决于复杂的变形参数\(u=(u_1,\ldots ,u_n)\)，这些参数是不规则奇点处的前导矩阵的特征值。同时，我们考虑了一个非归一化 Schlesinger 型表达 Fuchsian 系统等单性的 Pfaffian 系统，其极点是变形参数\(u_1,\ldots ,u_n\)。参数在包含不规则系统主矩阵特征值的合并轨迹的多圆盘中变化，对应于Fuchsian 奇点的汇合。我们构造等单向选择和奇异向量解决方案Fuchsian Pfaffian 系统及其等单向连接系数，因此扩展了 Balser 等人的结果。(I SIAM J Math Anal 12(5): 691–721, 1981) 和 Guzzetti (Funkcial Ekvac 59(3): 383–433, 2016) 到等单向性案例，包括奇点的汇合。然后，我们引入了所选向量解和奇异向量解的等单拉普拉斯变换，允许获得不规则系统的等单基本解，以及用连接系数表示的斯托克斯矩阵。这些事实，除了将（Balser 等人在 I SIAM J Math Anal 12(5): 691–721, 1981 中；Guzzetti 在 Funkcial Ekvac 59(3): 383–433, 2016 中）扩展到同向性案例（与聚结/汇合），允许通过拉普拉斯变换证明 Cotti 等人的主要结果。(Duke Math J arXiv:1706.04808, 2017)，即解析理论具有合并特征值的不规则系统的非通用等单向变形。