Rogue waves with rational profiles in unstable condensate and its solitonic model

TL;DR

This study numerically investigates rogue waves in unstable condensates, revealing their formation mechanism as multi-soliton interactions and showing that large rogue waves resemble scaled rational breather solutions.

Contribution

It demonstrates that rogue waves in unstable condensates are primarily formed through multi-soliton interactions and are well approximated by second-order rational breather solutions.

Findings

Large rogue waves exhibit similar properties in different models.

Multi-soliton interactions are key to rogue wave formation.

Rogue waves are well approximated by second-order rational breathers.

Abstract

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.