  Recently, under the assumption that the Doppler effect of the
relativistically expanding fireball surface is important, Qin et al. showed
that in most cases the power law relationship between the pulse width and
energy of gamma-ray bursts (GRBs)would exist in a certain energy range. We
check this prediction with two GRB samples which contain well identified
pulses. A power law anti-correlation between the full pulse width and energy
and a power law correlation between the pulse width ratio and energy are seen
in the light curves of the majority (around 65%) of bursts of the two samples
within the energy range of BATSE, suggesting that these bursts are likely to
arise from the emission associated with the shocks occurred on a
relativistically expanding fireball surface. For the rest of the bursts, the
relationships between these quantities were not predicted previously. We
propose to consider other spectral evolutionary patterns or other radiation
mechanisms such as a varying synchrotron or Comptonized spectrum to check if
the observed relationships for these rest bursts can also be accounted for by
the Doppler model. In addition, we find that the upper limits of the width
ratio for the two samples do not exceed 0.9, in agrement with what predicted
previously by the Doppler model. The plateau/power law/plateau and the peaked
features predicted and detected previously by Qin et al. are generally
observed, with the exceptions being noticed only in a few cases. According to
the distinct values of two power law indices of FWHM and ratio and energy, we
divide the bursts into three subsets which are located in different areas of
the two indices plane. We suspect that different locations of the two indices
might correspond to different mechanisms.
