Phase transitions in the two-lane density difference lattice hydrodynamic model of traffic flow

In this paper, we derive the KdV equation from the two-lane lattice hydrodynamic traffic model considering density difference effect. The soliton solution is obtained from the KdV equation. Under periodical boundary, the KdV soliton of traffic flow is demonstrated by numerical simulation. The numerical simulation result is consistent with the nonlinear analytical result. Under open system, the density fluctuation of the downstream last one lattice is designed to explore the empirical congested traffic states. A phase diagram is presented which includes free traffic, moving localized cluster, triggered stop-and-go traffic, oscillating congested traffic, and homogeneous congested traffic. Finally, the spatiotemporal evolution of all the traffic states described in phase diagram are reproduced. Results suggest that the two-lane density difference hydrodynamic traffic model is suitable to describe the actual traffic.