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

2022/10/27 by Liu, Lei, Sun, Wen-Rong, Malomed, Boris A. · 2 citations
#FOS: Physical sciences #Pattern Formation and Solitons (nlin.PS)

paper · doi:10.48550/arxiv.2210.15795

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.

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• Exact vector Akhmediev breathers dominated by a linearly stable frequency
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