Rogue Waves With Rational Profiles in Unstable Condensate and Its Solitonic Model

In this brief report we study numerically the spontaneous emergence of rogue waves in 1) modulationally unstable plane wave at its long-time statistically stationary state and 2) bound-state multi-soliton solutions representing the solitonic model of this state. 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.

Automated summary

The study indicates that the largest rogue waves in both systems have practically identical dynamical and statistical properties, suggesting that multi-soliton interaction may be the main mechanism for rogue wave formation in modulational instability cases. Additionally, it is demonstrated that most of the largest rogue waves can be well approximated by the amplitude-scaled rational breather solution of the second order in both space and time.