Two hierarchies of multi-component Kaup–Newell equations and theirs integrable couplings

Two hierarchies of multi-component Kaup–Newell equations are derived from an arbitrary order matrix spectral problem, including positive non-isospectral Kaup–Newell hierarchy and negative non-isospectral Kaup–Newell hierarchy. Moreover, new integrable couplings of the resulting Kaup–Newell soliton hierarchies are constructed by enlarging the associated matrix spectral problem.