In the framework of the model of a spatially nonuniform Bose-Einstein condensate with helicoidal spin-orbit (SO) coupling, we find abnormal Peregrine solitons (PSs) on top of flat and periodic backgrounds, with ultrahigh amplitudes. We explore the roles of the SO coupling strength and helicity pitch in the creation of these anomalously tall PSs and find that their amplitude, normalized to the background height, attains indefinitely large values. The investigation of the modulation instability (MI) in the same system demonstrates that these PSs exist in a range of relatively weak MI, maintaining the feasibility of their experimental observation.
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Ding et al. (2024) studied this question.
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