Nonlinear waves in an inhomogeneous quantum plasma

For an inhomogeneous quantum magnetoplasma system with density and temperature gradients, a two-dimensional nonlinear fluid dynamic equation is derived in the case where the collision frequency between ions and neutrals is minor. The shock, explosion and vortex solutions of the potential for this system are obtained. The changes of the potential in the dense astrophysical environment are discussed. It is shown that the strength of the shock and the width of the explosion are both enhanced with the density increasing (equivalently, the normalized quantum parameter decreasing), but with the drift velocity decreasing (equivalently, the density and temperature gradients decreasing); the potential always tends to a stable value with the spatiotemporal phase increasing, and the system approaches finally to a stable state. Besides, the temporal and spatial distributions of the vortex potential display a stable and period vortex street.