We consider a one-dimensional chain of particles sitting in two-dimensional anharmonic potentials. The statistical mechanics of this model in the continuum limit correspond to the Ginzburg-Landau theory with a complex order parameter. The dynamics of this model may describe the dynamics of incommensurate charge-density waves. The dynamic structure factor of this model is calculated using the molecular-dynamics technique. The spectrum can be interpreted in terms of a phase mode and an amplitude mode. We also investigate the effect of coupling to a random distribution of potentials. The main effect of these potentials is to pin the phase and push the phase mode to a finite frequency. We also investigate a simple model of dc conductivity due to the motion of the charge-density wave. We conclude that in the presence of strong random impurity potentials, the conductivity is activated with an activation energy of the order of the energy gap. As such its contribution to the total conductivity is insignificant. The origin of this activated conductivity is discussed in terms of phase slippage by the nucleation of zeros in the amplitude. © 1977 The American Physical Society.