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...

We analyze a system of reacting elements harmonically coupled to nearest neighbors in the continuum limit. An analytic solution is found for traveling waves. The procedure is used to find oscillatory as well as solitary waves. A comparison is made between exact solutions and solutions of the...