Rogue waves in nonlocal media

TL;DR

This paper explores rogue wave formation in nonlocal media described by a nonlinear Schrödinger equation, revealing increased rogue wave activity under certain conditions despite suppressed modulation instability.

Contribution

It identifies a parameter regime where rogue waves are enhanced in nonlocal media, differing from classical solutions, and provides numerical insights into their distinct nature.

Findings

Rogue wave amplitude and frequency increase in specific nonlocal regimes.

Suppression of modulation instability does not prevent rogue wave formation.

Numerical results show these rogue waves differ from classical Peregrine or soliton solutions.

Abstract

The generation of rogue waves is investigated via a nonlocal nonlinear Schrodinger (NLS) equation. In this system, modulation instability is suppressed and is usually expected that rogue wave formation would also be limited. On the contrary, a parameter regime is identified where the instability is suppressed but nevertheless the number and amplitude of the rogue events increase, as compared to the standard NLS (which is a limit of the nonlocal system). Furthermore, the nature of these waves is investigated; while no analytical solutions are known to model these events, numerically it is shown that they differ significantly from either the rational (Peregrine) or soliton solution of the limiting NLS equation. As such, these findings may also help in rogue wave realization experimentally in these media.