KINK SOLITON CHARACTERIZING TRAFFIC CONGESTION

We study traffic congestion by analyzing a one-dimensional traffic how model. Developing an asymptotic method to investigate the long time b ehavior near a critical point, we derive the modified Korteweg-de Vrie s (MKdV) equation as the lowest-order model. There is an infinite numb er of kink solitons to the MKdV equation, while it has been found by n umerical simulations that the kink pattern arising in traffic congesti on is uniquely determined irrespective of initial conditions. In order to resolve this selection problem,we consider higher-order correction s to the MKdV equation and find that there is a kink soliton that can deform continuously, with the perturbation represented by the addition of these corrections. With numerical confirmation, we show that this continuously deformable kink soliton characterizes traffic congestion. We also discuss the relationship between traffic congestion and the s lugging phenomenon in granular how.