The Newtonian dynamics of a one-dimensional system with a complex order parameter and an anharmonic potential energy of the Landau type is examined in a wide temperature range using numerical Monte Carlo–molecular dynamics simulations. Results are discussed with an emphasis on the incommensurate Peierls systems. Dispersive-mode behavior found previously in the quartic region near TMF can be followed to lower temperatures where the frequency of the phonon mode decreases and the damping increases. Below 0.4TMF the dynamic structure factor is characterized by the overdamped mode down to 0.3TMF, when the separation between the phase and the amplitude mode becomes effective. The relation between the different regimes in S(k,ω) and the pseudogap in the electronic spectrum is also briefly discussed
