Dynamics of the One-Dimensional Quartic System with a Complex Order Parameter

A one-dimensional system with anharmonic energy of the Landau type is considered. The motion of the system is governed by Newton's equations. It is shown that unexpectedly a dispersive mode describes the dynamics of this system near the mean-field transition temperature. The universal functions which describe the correlation in time and space are obtained by numerical simulations. The result applies in particular to the description of the 2kF mode softening (CDW formation) in quasi-one-dimensional compounds.