A novel kind of multi-component nonisospectral super soliton hierarchy with self-consistent sources

We construct a novel Lie superalgebra spl(2N,1) through the algebraic extension of the fundamental spl(2,1) structure. This mathematical framework enables the systematic generation of multi-component nonisospectral superintegrable hierarchies with self-consistent sources associated with the spl(2N,1) algebra. As principal applications, we establish two distinct classes of multi-component nonisospectral problems, from which we rigorously derive: (i) a multi-component nonisospectral super–Ablowitz–Kaup–Newell–Segur (AKNS) hierarchy, and (ii) a multi-component nonisospectral super-Dirac hierarchy. To elucidate the construction mechanism, we explicitly analyze the N=2 coupling case within these multi-component nonisospectral frameworks, thereby obtaining coupled nonisospectral super-AKNS and Dirac hierarchies with self-consistent sources. Furthermore, we investigate the super-Hamiltonian structures and conservation laws underlying these multi-component supersoliton hierarchies.