Rogue waves are considered as giant nonlinear waves in oceans and optics that suddenly appear from nowhere and disappear without a trace. We analyze their strange nature, dynamic generation, and modulation instability. We present rogue wave solutions to the standard and extended (Hirota and quintic) nonlinear Schrodinger equation that can model propagation phenomena in nonlinear optics. We also discuss the numerical procedure of mode pruning in order to suppress the modulation instability of rogue waves.
We demonstrate how to produce stable Talbot carpets (recurrent images of light) of rogue waves. The second approach of generating a double periodic array of high-intensity peaks, based on the matching of the Akhmediev breather periods to the period of elliptic background, is also discussed.
On the other side, one has to be cautious when a dynamic generation of rogue waves is considered since they can emerge as numerical artifacts, due to inadequate numerical treatment of modulation instability and homoclinic chaos.
Finally, we display how statistical analysis based on different numerical procedures can lead to misleading conclusions on the rogue waves' nature.