An extended car-following model based on intelligent transportation system application

The jams in the congested traffic reveal various density waves. Some of them are described by the nonlinear wave equations: the Korteweg–de-Vries (KdV) equation, the Burgers equation and the modified KdV equation. An extended car following model are proposed in previous work, and the kink-antikink solution has been obtained from the mKdV equation. We continue to derive the KdV equation near the neutral stability line by applying the reductive perturbation method. The traffic jam could be thus described by the soliton solution, and the analysis result is consistent with the previous one. From the numerical simulations results, the soliton waves are found, and traffic jam is suppressed efficiently as encounter big disturbances.