  We focused on the Ablowitz--Ladik equation on a zero background, specifically
considering the scenario of $N$ pairs of multiple poles. Our first goal was to
establish a mapping between the initial data and the scattering data. This
allowed us to introduce a direct problem by analyzing the discrete spectrum
associated with $N$ pairs of higher-order zeros. Next, we constructed another
mapping from the scattering data to a $2\times2$ matrix Riemann--Hilbert
problem equipped with several residue conditions set at $N$ pairs of multiple
poles. By characterizing the inverse problem based on this Riemann--Hilbert
problem, we were able to derive higher-order soliton solutions in the
reflectionless case. Furthermore, we expressed an infinite-order soliton
solution using a special Riemann--Hilbert problem formulation.
