Analytical Solution of Congested Traffic Pattern Formation for a Viscous High-Order Model
In this paper, a new viscous vehicular flow model proposed by Song et al is discussed from the perspective of the capability to reproduce nonlinear traffic behavors observed in real traffic. The linear stability condition for stationary and equilibrium flow is derived. Near the neutral stability curve, the Korteweg–de Vries (KdV) equation describing congested traffic pattern is derived with use of the reduction perturbation method. And the corresponding analytical soliton solution is obtained.
X. L. Li et al., "Analytical Solution of Congested Traffic Pattern Formation for a Viscous High-Order Model", Applied Mechanics and Materials, Vols. 97-98, pp. 546-549, 2011