Vector rogue waves with an unusual number in a coupled Gross–Pitaevskii equation

The extreme destructive potential of optical rogue waves has long posed a major challenge to the safe and stable operation of fiber-optic systems. To reduce the occurrence frequency of rogue waves, we investigate a vector rogue wave solution of a coupled Gross–Pitaevskii equation. By combining similarity transformation and generalized Darboux transformation, we obtained higher-order rogue wave solutions with an unusual number. Through numerical simulation, we tested the stability of the vector rogue waves and verified their feasibility through numerical experiments. By controlling the relevant parameters, we could increase the stability of higher-order vector rogue waves and reduce their number. This type of higher-order rogue wave with an unusual number can reduce the frequency of high-energy ultrashort waves that occur in optical devices, thereby helping to mitigate the damage caused by rogue waves to optical equipment.