  Electric field induced collective reorientation of nematic molecules placed
between two flat parallel electrodes is of importance for both fundamental
science and practical applications. This reorientation is either homogeneous
over the area of electrodes, as in liquid crystal displays, or periodically
modulated, as in the phenomenon called electroconvection1, similar to
Rayleigh-B\'enard thermal convection. The question is whether the electric
field can produce spatially localized propagating solitons of molecular
orientation. Here we demonstrate electrically driven three-dimensional
particle-like solitons representing self-trapped waves of oscillating molecular
orientation. The solitons propagate with a very high speed perpendicularly to
both the electric field and the initial alignment direction. The propulsion is
enabled by rapid collective reorientations of the molecules with the frequency
of the applied electric field and by lack of fore-aft symmetry. The solitons
preserve spatially-confined shapes while moving over distances hundreds of
times larger than their size and survive collisions. During collisions, the
solitons show repulsions and attractions, depending on the impact parameter.
The solitons are topologically equivalent to the uniform state and have no
static analogs, thus exhibiting a particle-wave duality. We anticipate the
observations to be a starting point for a broad range of studies since the
system allows for a precise control over a broad range of parameters that
determine the shape, propagation speed, and interactions of the solitons.
