Signature of second stable regime of modulational instability and rogue wave triplets in dual-polarity dusty plasmas

This work presents a theoretical and numerical investigation of the modulational instability and rogue wave triplets of dust-acoustic waves in a dusty plasma composed of warm adiabatic dust grains with opposite polarity, q-nonextensive electrons, and nonthermal ions. The dynamics are modeled by deriving a nonlinear Schrödinger (NLS) equation using the reductive perturbation method. This equation leads to the growth rate of modulational instability of dust-acoustic waves. The analysis reveals that positively charged dust grains, the degree of electron nonextensivity, and the distribution of electrons (protons) on negatively (positively) charged dust grains critically influence the growth rate of instability. The ratio of dispersion to nonlinear coefficients in the NLS equation demarcates stable and unstable regions, distinguishing bright and dark solitons. This novel mechanism reveals a second stability regime in opposite polarity dusty plasma for the fast acoustic mode. We also explore the impacts of multiple physical parameters, which are sensitive in forming rogue wave triplets. These parameters result in three distinct peaks arranged in a triangular pattern, with unique rotational behavior that offers a new perspective on the dynamical behaviors of localized nonlinear waves. To validate the model, we benchmark the exact analytical solutions for rogue wave triplets with numerical results. This comparison demonstrates the accuracy of the model and provides deeper insight into nonlinear localized waves. This analysis has significant implications for rogue wave triplet formation in both space and laboratory plasma environments. These triplets may coalesce into super freak waves under specific conditions, particularly when key physical parameters approach zero.