Drift shocks, explosions and vortices in inhomogeneous quantum magnetoplasma

For an inhomogeneous quantum magnetoplasma, a two-dimensional nonlinear equation is derived considering that the collision between ions and neutrals is dominant. The dispersion relation shows that the quantum parameter modifies the scale length of the system, and the real and imaginary frequency are related to the drift and collision frequency, respectively. Drift shock and explosion solutions reveal that the strength of shock and the width of explosion enhance with the increase of density and drift velocity, but with the decrease of the collision frequency; the distributions of potential tend to a stable state with the spatio-temporal phase increasing. The distributions of the vortex potential display a vortex street. The quantum parameter and drift velocity affect the stability of the system.