  Solitons in liquid crystals have generated considerable interest. Several
hypotheses of varying complexity have been advanced to explain how they emerge,
and a consensus has not emerged yet about the underlying forces responsible for
their formation or their structure. In this work, we present a minimal model
for soliton structures in achiral nematic liquid crystals, which reveals the
key requirements needed to generate traveling solitons in the absence of added
charges. These include a surface imperfection or inhomogeneity capable of
producing a twist, flexoelectricity, dielectric contrast, and an applied AC
electric field that can couple to the director's orientation. Our proposed
model is based on a tensorial representation of a confined liquid crystal, and
it predicts the formation of "butterfly" structures, quadrupolar in character,
in regions of a slit channel where the director is twisted by the surface
imperfection. As the applied electric field is increased, solitons (or
"bullets") become detached from the wings of the butterfly, which then rapidly
propagate throughout the system. The main observations that emerge from the
model, including the formation and structure of butterflies, bullets, and
stripes, as well as the role of surface imperfections and the strength of the
applied field, are consistent with our own experimental findings presented here
for nematic LCs confined between two chemically treated parallel plates.
