  In the framework of the model of a spatially non-uniform Bose-Einstein
condensate with helicoidal spin-orbit (SO) coupling, we find abnormal Peregrine
solitons (PSs) on top of flat and periodic backgrounds, with ultra-high
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.
