  A recent study by Posselt et al. (2017) reported the deepest X-ray
investigation of the Geminga pulsar wind nebula (PWN) by using \emph{Chandra
X-ray Observatory}. In comparison with previous studies of this system, a
number of new findings have been reported and we found these suggest the
possible variabilities in various components of this PWN. This motivates us to
carry out a dedicated search for the morphological and spectral variations of
this complex nebula. We have discovered variabilities on timescales from a few
days to a few months from different components of the nebula. The fastest
change occurred in the circumstellar environment at a rate of 80 per cent of
the speed of light. One of the most spectacular results is the wiggling of a
half light-year long tail as an extension of the jet, which is significantly
bent by the ram pressure. The jet wiggling occurred at a rate of about 20 per
cent of the speed of light. This twisted structure can possibly be a result of
a propagating torsional Alf\`{v}en wave. We have also found evidence of
spectral hardening along this tail for a period of about nine months.
