Non-isospectral integrable couplings of Ablowitz–Ladik hierarchy with self-consistent sources

A kind of new non-isospectral integrable couplings of discrete soliton equations hierarchy with self-consistent sources associated with sl˜(4) is presented. As an application example, the integrable coupling hierarchy of non-isospectral Ablowitz–Ladik with self-consistent sources is derived by using of the loop algebra sl˜(4).