This study investigates the nonlinear dynamics and stability of dust-acoustic waves (DAWs) in a magnetized three-component dusty plasma comprising cold negative dust impurities and superthermally distributed cold/hot positive ions. By employing a reductive perturbation technique, a (3+1)-dimensional Zakharov-Kuznetsov (ZK) equation is derived, governing the evolution of compressive solitons. Numerical analyses reveal that the phase velocity of DAWs increases with the spectral indices ( \( \kappa _{c} \) and \( \kappa _{h} \) ) of cold and hot ions, attributed to reduced Landau damping, but decreases with higher cold-to-hot ion temperature ratios ( \( \theta \) ) and density ratios ( \( \mu \) ), due to enhanced ion drag and thermal damping. Solitary wave amplitudes grow with lower \( \mu \) , \( \theta \) , and \( \kappa _{c} \) while widths broaden with increasing \( \kappa _{c} \) and \( \kappa _{h} \) . The nonlinear term’s negativity confirms compressive solitons, with modulating their energy by the magnetic field strength ( \( \Omega \) ) and propagation angle ( \( \delta \) ). Instability growth rates escalate with higher electron densities and magnetic gradients, linked to current-driven turbulence. These findings elucidate wave behavior in astrophysical environments (e.g., cometary tails, planetary rings) and laboratory setups, particularly in fusion devices where superthermal particles and magnetic confinement govern plasma stability.
