  We explore theoretically how to tune the dynamics of a quasi one-dimensional
harmonically trapped Bose-Einstein condensate (BEC) due to an additional red-
and blue-detuned Hermite-Gaussian dimple trap (HGdT). To this end we study a
BEC in a highly non-equilibrium state, which is not possible in a traditional
harmonically confined trap. Our system is modeled by a time-dependent
Gross-Pitaevskii equation, which is numerically solved by the Crank-Nicolson
method in both imaginary and real time. For equilibrium, we obtain a condensate
with two bumps/dips which are induced by the chosen TEM$_{01}$ mode for the
red/blue-detuned HGdT, respectively. Afterwards, in time-of-flight dynamics, we
examine the adherence/decay of the two bumps/dips in the condensate, which are
induced by the still present red/blue-detuned HGdT, respectively. On the other
hand, once the red/blue HGdT potential is switched off, shock-waves or
bi-trains of gray/dark pair-solitons are created. During this process it is
found that the generation of gray/dark pair-solitons bi-trains are generic
phenomena of collisions of moderately/fully fragmented BEC. Additionally, it
turns out that the special shape of generated solitons in the harmonically
trapped BEC firmly depends upon the geometry of the HGdT.
