Asymptotic solutions for a multi-anticipative car-following model

Using a long wave expansion we study the asymptotic solutions near a critical point of a multi-anticipative car-following model. A suitable rescaling of the variables then yields a modified Korteweg–de Vries (MKdV) equation with higher order corrections. An equation of this general form has already been investigated in detail in case of a simple model which allows us to use these results. We are thus led to the conclusion that the characteristic features of the multi-interaction model in the congested state can be obtained from the simple model by appropriately scaling the results.