We propose methods to generate and manipulate vortex dipoles in an atomic Bose-Einstein condensate using Gaussian beams of red-or blue-detuned laser. Vortex dipoles with controlled velocities are shown to be created and launched by a red-detuned beam and by two blue-detuned beams. Critical beam velocities for the vortex nucleation are investigated. The launched vortex dipoles can be trapped, curved, accelerated, and decelerated by using Gaussian laser beams. Collisions between vortex dipoles are demonstrated.

The interfacial instability and subsequent dynamics in a phase-separated two-component Bose-Einstein condensate with rotational symmetry are studied. When the interatomic interaction or the trap frequency is changed, the Rayleigh-Taylor instability breaks the rotational symmetry of the interface, which is subsequently deformed into nonlinear patterns including mushroom shapes.

The dynamics of an exciton-polariton superfluid resonantly pumped in a semiconductor microcavity are investigated by mean-field theory. Modulational instability develops into crystalline order, and then, ordered and disordered states alternately form. It is found that the crystalline order at rest can coexist with superflow.

The dynamics of a vortex dipole in a quasi-two dimensional two-component Bose-Einstein condensate are investigated. A vortex dipole is shown to penetrate the interface between the two components when the incident velocity is sufficiently large. A vortex dipole can also disappear or disintegrate at the interface depending on its velocity and the interaction parameters.

It is shown using numerical simulations that flow patterns around an obstacle potential moving in a superfluid exhibit hysteresis. In a certain velocity region, there is a bistability between stationary laminar flow and periodic vortex shedding. The bistability exists in two and three dimensional systems.