Stabilization analysis and modified Korteweg-de Vries equation in a cooperative driving system

Two lattice traffic models are proposed by incorporating a cooperative driving system. The lattice versions of the hydrodynamic model of traffic flow are described by the differential-difference equation and difference-difference equation, respectively. The stability conditions for the two models are obtained using the linear stability theory. The results show that considering more than one site ahead in vehicle motion leads to the stabilization of the system. The modified Korteweg-de Vries equation (the mKdV equation, for short) near the critical point is derived by using the reductive perturbation method to show the traffic jam which is proved to be described by kink-anti-kink soliton solutions obtained from the mKdV equations.