Soliton and kink jams in traffic flow with open boundaries

Soliton density :wave is investigated numerically and analytically in the o ptimal velocity model (a car-following model) of a one-dimensional traffic flow with open boundaries. Soliton density wave is distinguished from the k ink density wave. It is shown that the soliton density wave appears only at the threshold of occurrence of traffic jams. The Korteweg-de Vries (KdV) e quation is derived from the optimal velocity model by the use of the nonlin ear analysis. It is found that the traffic soliton appears only near the ne utral stability line. The soliton solution is analytically obtained from th e perturbed KdV equation. It is shown that the soliton solution obtained fr om the nonlinear analysis is consistent with that of the numerical simulati on. [S1063-651X(99)04807-2].