A systematic determination of when discrete Kuznetsov-Ma (KM) breather solutions of the defocusing Ablowitz-Ladik lattice, built on an arbitrarily large constant background, are non-singular for all times, giving explicit conditions on the background amplitude and spectral parameters. It introduces a novel regular KM-type breather, uses Darboux transformations to construct multi-KM (double) breathers with regular parameter regimes, connects the small-frequency limit to rogue-wave profiles, and studies stability numerically, including destabilization by modulational instability of the background.
Boadi, Charalampidis, Kevrekidis, Ossi and Prinari study discrete analogs of Kuznetsov-Ma (KM) breathers on the defocusing Ablowitz-Ladik (AL) lattice sitting on an arbitrarily large constant backgro…