Strong Symmetries of Non-Isospectral Ablowitz–Ladik Equations

For each non-isospectral Ablowitz–Ladik equation a strong symmetry operator is given. The strong symmetry contains time variable explicitly and by means of it two sets of symmetries are generated. Functional derivative formulae between the strong symmetry and symmetries are derived, by which the obtained symmetries are shown to compose a centerless Kac–Moody–Virasoro algebra. Master symmetries for non-isospectral Ablowitz–Ladik equations are also discussed.