Exciting extreme events in the damped and AC-driven NLS equation through plane-wave initial conditions.

We investigate, by direct numerical simulations and for certain parametric regimes, the dynamics of the damped and forced nonlinear Schrödinger (NLS) equation in the presence of a time-periodic forcing. It is thus revealed that the wave number of a plane-wave initial condition dictates the number of emerged Peregrine-type rogue waves at the early stages of modulation instability. The formation of these events gives rise to the same number of transient "triangular" spatiotemporal patterns, each of which is reminiscent of the one emerging in the dynamics of the integrable NLS in its semiclassical limit, when supplemented with vanishing initial conditions.