标题： 弗罗利赫-尼延豪斯几何与可积矩阵偏微分方程系统 显示英文标题

标题： Frölicher-Nijenhuis geometry and integrable matrix PDE systems

摘要： 给定一个光滑n维流形M上的两个(1,1)型张量场，它们的所有Frolicher-Nijenhuis括号都消失，那么M上的微分形式代数成为一个双微分分次代数。 作为结果，与之相关联的是部分微分方程（PDE）系统，这些系统作为线性方程组的可积性条件出现，并具有二元达布变换来生成精确解。 我们恢复了手征模型和自对偶杨-米尔斯方程的势形式，以及到四维以上维度的相应推广，并得到了新的可积的非自治非线性矩阵PDE及其相应系统。 显示英文摘要

摘要： Given two tensor fields of type (1,1) on a smooth n-dimensional manifold M, such that all their Fr\"olicher-Nijenhuis brackets vanish, the algebra of differential forms on M becomes a bi-differential graded algebra. As a consequence, there are partial differential equation (PDE) systems associated with it, which arise as the integrability condition of a system of linear equations and possess a binary Darboux transformation to generate exact solutions. We recover chiral models and potential forms of the self-dual Yang-Mills, as well as corresponding generalizations to higher than four dimensions, and obtain new integrable non-autonomous nonlinear matrix PDEs and corresponding systems.