  In this brief report we study numerically the spontaneous emergence of rogue
waves in (i) modulationally unstable plane wave at its long-time statistically
stationary state and (ii) bound-state multi-soliton solutions representing the
solitonic model of this state [Gelash et al, PRL 123, 234102 (2019)]. Focusing
our analysis on the cohort of the largest rogue waves, we find their
practically identical dynamical and statistical properties for both systems,
that strongly suggests that the main mechanism of rogue wave formation for the
modulational instability case is multi-soliton interaction. Additionally, we
demonstrate that most of the largest rogue waves are very well approximated --
simultaneously in space and in time -- by the amplitude-scaled rational
breather solution of the second order.
