Nonlinear waves on the surface of a dielectric liquid in a horizontal electric field in 3D geometry: Exact solutions

It has been shown that waves of arbitrary configuration in 3D geometry may propagate without distortion along the surface of a dielectric liquid in the direction of a horizontal electric field. This situation occurs for the high-permittivity liquids in the case of a sufficiently high external field when the effect of electrostatic forces dominates. A general solution of the equations of motion that describes the interaction of counterpropagating waves of a small but finite amplitude has been obtained.