In this paper, we study the dynamic and infrared activity of pure trans- and cis-polyacetylene, doped systems, and systems with cis-trans defects. First we study the behaviour of the Goldstone mode frequency of a simple linear chain. We find that this frequency depends strongly on the value of the dimerization parameter u, in contrast with the experimental results, where this mode is particularly stable. Thus, taking u as a free parameter, we develop several realistic models for neutral perfect cis and trans chains and doped systems. Our results are in very good agreement with experimental results. We show that for the doped chain the transverse component of conductivity is about 1% of the longitudinal component. The presence of the cis-trans defect allows us to give the origin of several peaks found experimentally and not interpreted until now. We show that in the presence of cis-trans defects the photoinduced infrared activity may appear in systems with charged solitons and antisolitons on the same neutral chain. Computed results are also in very good agreement with the experimental data.