  Liquid crystal skyrmions are topologically protected spatially localized
distortions of the director field which are fascinating from both fundamental
mathematics and applied physics points of view. Skyrmions are realized in
experimental setups which are identical to those used in display technology.
This opens exciting opportunities for designing advanced electro-optical
applications. Skyrmions exhibits particle-like properties including
translational motion in time periodic electric fields. Despite a large volume
of experimental results on the skyrmion collective behaviour, the theoretical
understanding of their effective interactions and emerging dynamics is rather
limited due to computational heaviness of numerical models based upon fine
grained Frank-Oseen or Landau-de Gennes continuum approaches. Here, we develop
a coarse grained model of the skyrmion dynamics. The model reveals the
underpinning physical mechanism of the skyrmion motion driven by pulse width
modulated electric fields. The mechanism is based upon the complex dynamics of
the width of the twist wall around the skyrmion's core. The width evolves in a
non-reciprocal way within each on and off states of the field, resulting in a
net displacement of the skyrmion. We analyse in details the average skyrmion
velocity as a function of the frequency and strength of the field as well as
its duty cycle. The model predictions agrees qualitatively with the results of
experiments and full numerical minimization of the fine grained models. Our
results provide insights into the conditions necessary to observe velocity
reversal as a function of the field parameters.
