Strong symmetries for the four-potential non-isospectral Ablowitz–Ladik equations

The strong symmetry for each four-potential non-isospectral Ablowitz–Ladik (AL) equation is given explicitly. Two sets of symmetries for the non-isospectral AL hierarchy can be generated by the strong symmetry acting on the elementary symmetries. The obtained symmetries are proved to satisfy the Lie algebraic structure by means of functional derivative formulae. Furthermore, under the reduction of the potentials, the strong symmetry of each even order member of the non-isospectral hierarchy can be reduced to the two potential case. (paper)