Traveling waves in ferroelectric smectic-C liquid crystals.

This article investigates, by means of Lie point symmetries, traveling wave solutions to a dynamic equation that frequently arises in the theory of ferroelectric smectic- C liquid crystals under the influence of an electric field. The equation considered has three sinusoidal nonlinearities and possible time-dependent solutions are discussed in the context of minima and maxima of the electric energy density for these liquid crystals: solutions travel between such constant equilibrium states. Implicit solutions to an approximation of the governing dynamic equation are determined. Nondimensional control parameters that characterize changes in the availability of equilibrium states as the magnitude of the field increases are also identified.