Modified KdV equation for jamming transition in the continuum models of traffic

摘要: Abstract Continuum models of traffic are proposed to describe the jamming transition in flow on a highway. They simplified versions hydrodynamic model traffic. Two continuum presented: one is described by partial differential equations and other discrete lattice version. The linear stability theory nonlinear analysis applied models. modified Korteweg–de Vries equation (KdV) near critical point derived using reduction perturbation method. It shown that density wave congested KdV equation. solutions obtained from two compared with optimal velocity (car following model).