New non-isospectral integrable couplings of the AKNS system

By means of semi-direct sums of Lie algebras and the compatibility condition of Lax pair, an efficient way to construct non-isospectral integrable couplings is proposed. As its applications, new non-isospectral integrable couplings of the AKNS system are obtained. The method can be devoted to constructing non-isospectral integrable couplings of other nonlinear evolution equations.