  We study the asymptotics for the Ablowitz-Ladik equation. By taking
appropriate continuum limits, it can be shown that the behavior of the equation
near degenerate frequencies is well approximated by a complex modified
Korteweg-de Vries equation. Using this connection, we use the method of
space-time resonances to derive a description of the modified scattering
behavior of the Ablowitz-Ladik equation, which includes two regions where the
solution behaves like a self-similar solution to the complex mKdV equation.
