Traac Jams, Granular Ow, and Soliton Selection

The ow of traac on a long section of road without entrances or exits can be modelled by continuum equations similar to those describing uid ow. In a certain range of traac density, steady ow becomes unstable against the growth of a cluster, or \phantom" traac jam, which moves at a slower speed than the otherwise homogeneous ow. We show that near the onset of this instability, traac ow is described by a perturbed Korteweg-deVries equation. The traac jam can be identiied with a soliton solution of the KdV equation. The perturbation terms select a unique member of the continuous family of KdV solitons. These results may also apply to the dynamics of granular relaxation.