Abstract We define new matrix fourth Painleve hierarchies and a new matrix second Painleve hierarchy. For our matrix fourth Painleve hierarchies, properties such as auto-Backlund transformations, Backlund transformations and special integrals are derived, and known relations between fourth Painleve transformations are extended to the matrix ODE hierarchies. The matrix ODE hierarchies presented here are derived as reductions of a new nonisospectral matrix dispersive water wave hierarchy and modifications thereof.

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关于矩阵四 Painlevé 层次结构

摘要 我们定义了新的矩阵第四 Painleve 层次结构和一个新的矩阵第二 Painleve 层次结构。对于我们的矩阵第四 Painleve 层次结构，导出了诸如自动贝克兰德变换、贝克兰德变换和特殊积分等属性，并将第四Painleve 变换之间的已知关系扩展到矩阵 ODE 层次结构。此处介绍的矩阵 ODE 层次是作为新的非等谱矩阵色散水波层次及其修改的简化而导出的。