The effects of wind and nonlinear damping on rogue waves and permanent downshift

The proximity of the initial data to unstable plane waves impacts the characteristic features of the rogue waves in the nonlinear damped HONLS evolution. We find that as the initial data is chosen closer to the plane wave, the maximum strength, number, and lifetime of rogue waves increase while the time of permanent downshift decreases. Alternatively, we show that the greater the wave strength, the more rogue waves, or the longer their lifetime, the earlier permanent downshift occurs.