Akhmediev, Nail; Ankiewicz, Adrian
We study modulation instability (MI) of the discrete constant-background wave of the Ablowitz-Ladik (A-L)
equation. We derive exact solutions of the A-L equation which are nonlinear continuations of MI at longer
times. These periodic solutions comprise a family of two-parameter solutions with an arbitrary background
field and a frequency of initial perturbation. The solutions are recurrent, since they return the field state to the
original constant background solution after the process of...[Show more]
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