Exact solutions to the nonlinear equation in traffic congestion

In this paper, the KdV-mKdV equation is obtained via the reductive perturbation method which can be applied to model the traffic flow. To overcome the shortcomings of the traditional KdV-mKdV equation, the original equation is converted into a space-time fractional equation, which is decreased to a common differential equation by using fractional complex transformation. All possible exact solutions are given through the entire discrimination gadget for polynomial method. In particular, the corresponding options are resembled for the specific parameters to show that each answer in the classification can be realized. And the numerical simulations in the paper additionally confirm this conclusion.