A stability analysis is carried out for a known exact traveling wave solution to a dynamic equation with sinusoidal nonlinearities, which arises in the study of smectic-C liquid crystals. The analysis is set in the usual context of traveling wave stability where suitably small perturbations may induce a phase shift to the original traveling wave. A control parameter beta, which is related to the physical properties of the liquid crystal and the applied electric field, determines the possibility of a phase shift and characterizes the possible oscillatory or monotonic decay of the perturbations; these properties are derived from the spectrum of the perturbation equation. The consequences of these results are discussed for a smectic-C liquid crystal under the influence of an applied electric field tilted to the planes of the smectic layers and for a problem arising in chiral smectic-C liquid crystals. [References: 27]
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