Abstract
Electrons in space plasma may follow vortex-like distribution, that is why we have derived the three-dimentional (3D) nonlinear modified Zakharov-Kuznetsov (mZK), describing the propagation of dust acoustic solitary to the plasma system composed of four components, magnetized charged dust plasma with electrons modelled by vortex-like distribution. By using the reductive perturbation method, it has been found that both solitary wave amplitude and width are affected by the plasma parameters: graim charge ratio ρ, population parameter β, and temperature ratio σ. The small-k perturbation technique has also been applied to study the instability criterion and growth rate of this instability. Cyclotron frequency Ω, temperature ratio
, direction cosine (
and
), and grain charge ratio ρ are found to modify the instability growth rate Γ.