Abstract
We propose a method for generating higher-dimensional nonisospectral super integrable coupling hierarchies associated with a new type of higher-dimensional Lie superalgebra. As applications, we introduce a coupled and a multi-component super Dirac spectral problems respectively, and thus deduce a coupled generalized super integrable Dirac hierarchy and a multi-component generalized super integrable Dirac hierarchy. Additionally, we discuss the super Hamiltonian structures of the resulting higher-dimensional super Dirac hierarchies.
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