  This paper suggests a method for an experiment to create dark soliton-like
waves in a trapped atomic Bose-Einstein condensate (BEC). With the phase
imprinting method, a soliton-like disturbance is produced along the x-axis. The
method is used in two cases (with and without rotation of an asymmetric
trapping potential). The disturbance in a two-dimensional system is unstable.
The soliton-like perturbation is found to decay into more stable vortex pairs
together with a burst of sound wave. The simulations are performed by solving
the two-dimensional Gross-Pitaevskii equation (2D GPE). The successive dynamics
of the wave function are studied by monitoring the evolution of density and
phase profile.
