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Production of stable multidimensional solitary waves is a grand challenge in modern science. Steering their propagation is an even harder problem. Here we demonstrate three-dimensional solitary waves in a nematic, trajectories of which can be steered by the electric field in a plane perpendicular to the field. The steering does not modify the properties of the background that remains uniform. These localized waves, called director bullets, are topologically unprotected multidimensional solitons of (3 + 2)D type that show fore-aft and right-left asymmetry with respect to the background molecular director; the symmetry is controlled by the field. Besides adding a whole dimension to the propagation direction and enabling controlled steering, the solitons can lead to applications such as targeted delivery of information and micro-cargo.

Electric field-induced collective reorientation of nematic molecules is of importance for fundamental science and practical applications. This reorientation is either homogeneous over the area of electrodes, as in displays, or periodically modulated, as in electroconvection. The question is whether spatially localized three-dimensional solitary waves of molecular reorientation could be created. Here we demonstrate that the electric field can produce particle-like propagating solitary waves representing self-trapped “bullets” of oscillating molecular director. These director bullets lack fore-aft symmetry and move with very high speed perpendicularly to the electric field and to the initial alignment direction. The bullets are true solitons that preserve spatially confined shapes and survive collisions. The solitons are topologically equivalent to the uniform state and have no static analogs, thus exhibiting a particle–wave duality. Their shape, speed, and interactions depend strongly on the material parameters, which opens the door for a broad range of future studies.