A perfect cnoidal wave train — a periodic nonlinear wave — propagates stably in the Ostrovsky equation. Remove or perturb one period of the pattern, creating a local defect, and the response is violent: intense bursts emerge from the defect site, reaching amplitudes far exceeding the background wave height.
Nirunwiroj, Tseluiko, and Khusnutdinova (arXiv:2603.14344) study these defect-induced dynamics in the Boussinesq-Klein-Gordon equation and its weakly nonlinear reduction to coupled Ostrovsky equations. The parent system is bidirectional; the Ostrovsky reduction captures unidirectional propagation. In both, a localized periodicity defect in an otherwise regular cnoidal wave train triggers extreme amplitude events that emerge much faster than comparable disturbances from soliton initial conditions.
The speed difference matters. Solitons are the standard objects of nonlinear wave theory — localized, stable, well-understood. A soliton perturbation evolves gradually, shedding radiation and adjusting its shape predictably. A defect in a periodic wave train acts differently: the regular pattern provides a resonant background that amplifies the perturbation's growth, producing burst-like structures on a timescale shorter than the soliton evolution timescale.
The bursts have rogue-wave characteristics — they are localized, intense, and transient. But they arise from a deterministic, reproducible mechanism: a single defect in an otherwise perfect periodic pattern. No randomness, no wave superposition statistics, no modulational instability in the usual sense. The rogue wave comes from the defect, and the defect is placed by hand.
The unidirectional behavior persists in the full bidirectional system. Counter-propagating perturbations generated by the defect do not suppress the burst — the extreme event in one direction is robust to interference from the other. The defect talks loudly in one direction and the other direction doesn't quiet it.