Numerical simulation of soliton and kink density waves in traffic flow with periodic boundaries

The soliton and kink–antikink density waves are simulated with periodic boundaries, by adding perturbation in the initial condition on single-lane road based on a car-following model. They are reproduced in the form of the space–time evolution of headway, both of which propagate backwards. It is found that the solitons appear only near the neutral stability line regardless of the boundary conditions, and they exhibit upward form when the initial headway is smaller than the safety distance, otherwise they exhibit downward form. Comparison is made between the numerical and analytical results about the amplitude of kink–antikink wave, and the underlying mechanism is analyzed. Besides, it is indicated that the maximal current of traffic flow increases with decreasing safety distance. The numerical simulation shows a good agreement with the analytical results.