  We explore the energy dynamics of a two dimensional (2D) trapped
Bose-Einstein condensate (BEC) excited by a moving red-detuned laser potential
(RDLP). The trap is a combination of a power-law (PL) potential cutoff by a
hard-wall box potential (HWBP). It is found that by a restricted measurment of
the energy within the boundaries of the HWBP, the energy demonstrates
oscillations indicative of solitons. It is then demonstrated, that the geometry
of the PL potential influences the lifetime of these oscillations, i.e., the
lifetime of the ensuing solitons inside the HWBP. We argue that the energy
dynamics in this setup are a good tool for measuring their lifetime. It is also
found, that the condensate density dynamics display oscillatory patterns of a
magnitude and order controlled by the velocity of the RDLP. A connection to
oscillations in the chemical potential dynamics is also discussed. Essentially,
we suggest future experiments for this kind of setup, which would measure the
phonon energy dynamics to trace the lifetime of solitons.
