TDGL and mKdV equations for car-following model considering traffic jerk

A new traffic flow model is proposed based on an optimal velocity car-following model, which takes the traffic jerk effect into consideration. The nature of the model is researched by using linear and nonlinear analysis method. In traffic flow, the phase transition and the critical phenomenon which are described by the thermodynamic theory. The time-dependent Ginzburg-Landau (TDGL) equation and the modified Korteweg-de Veris (mKdV) equation are derived to describe the traffic flow near the critical point. In addition, the connection between the TDGL and the mKdV equations is also given. Numerical simulation is given to demonstrate the theoretical results.