Formation of rogue waves and modulational instability with zero-wavenumber gain in multi-component systems with coherent coupling

TL;DR

This paper investigates rogue wave formation through modulational instability with zero-wavenumber gain in multi-component systems, revealing a linear relation between MI gain and perturbation wavenumber as a key mechanism.

Contribution

It identifies a novel rogue wave formation mechanism involving zero-wavenumber gain in multi-component systems with coherent coupling, expanding understanding of rogue wave generation.

Findings

Rogue waves are generated by MI with zero wavenumber gain.

The mechanism requires a linear relation between MI gain and small wavenumber.

Applicable to multi-component systems like the massive Thirring model.

Abstract

It is known that rogue waves (RWs) are generated by the modulational instability (MI) of the baseband type. Starting with the Bers-Kaup-Reiman system for three-wave resonant interactions, we identify a specific RW-building mechanism based on MI which includes zero wavenumber in the gain band. An essential finding is that this mechanism works solely under a linear relation between the MI gain and a vanishingly small wavenumber of the modulational perturbation. The same mechanism leads to the creation of RWs by MI in other multi-component systems-in particular, in the massive Thirring model.