  We numerically study the impact of Gaussian barrier height and width on the
gray solitons population in a symmetric and asymmetric potential trap. The gray
solitons are created in a double-well potential by the density engineering
method. Two identical Bose-Einstein condensate fragments are confined and made
to collide by switching off the Gaussian barrier in a double-well potential. We
find that the gray solitons population can be manipulated by Gaussian barrier
height and width. We also study the gray solitons population dependence on the
coupling strength. Moreover, we also study the impact of an asymmetry present
in the double-well potential. We observe that such an asymmetry always swings
the point of collision of the gray solitons. Later, a stationary dark soliton
is created by the phase imprinting method and we observe that the initial
asymmetry in the double-well potential trap sets the dark soliton into
oscillation.
