  We study the time evolution processes of non-Hermitian systems under the open
boundary condition and confirm that the dynamical skin effect exists in
non-Hermitian systems analytically, and unveil the mechanism of its formation,
which is caused by both the non-Hermitian skin effect and the Hermitian wave
packet spreading. Furthermore, we find that in contrast to the uniform speed
motion in Hermitian situations, the Gaussian wave packet can be accelerated and
amplified during its time evolution in non-Hermitian systems. This additional
motion is found to be responsible for the dynamic skin effect.
