Density waves in the full velocity difference model

Abstract

Density waves are investigated in the full velocity difference model (FVDM) analytically and numerically. By the use of nonlinear analysis, the Burgers, Korteweg–de Vries (KdV) and Modified KdV equations are derived for the triangular shock wave, the soliton wave and the kink–antikink wave, respectively, appearing in the stable region out of the coexisting curve, near the spinodal line, and in the unstable region within the spinodal line. It is shown, numerically, that the triangular shock wave and the soliton wave are determined by the initial perturbation configuration and different initial perturbations will produce different waveforms in the stable region or near the spinodal line.