Density waves in the continuum analog of the full velocity difference model

A continuum version of the car-following full velocity difference model (FVDM) is developed using a series expansion of the headway in terms of the density. This continuum model obeys the equivalent stability criterion as its discrete counterpart, and the Burgers and Korteweg-de Vries equations deriving from the analogous continuum model are equivalent to their counterparts from the transformed car-following model.