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Modulation instability, Fermi-Pasta-Ulam recurrence, rogue waves, nonlinear phase shift, and exact solutions of the Ablowitz-Ladik equation

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]

CollectionsANU Research Publications
Date published: 2011-04-20
Type: Journal article
Source: Physical Review E
DOI: 10.1103/PhysRevE.83.046603


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