Publication

Abstract : In this paper, we investigate the traffic flow model with congested phase through local and nonlocal symmetry analysis. Firstly, we derive the Lie group of transformations and show that it admits four one-dimensional optimal algebras. Next, by similarity reductions, we construct several exact solutions for each subalgebras as well as analyze the relation of group parameters. Furthermore, we construct a tree representing nonlocally related partial differential equations (PDEs) consisting inverse potential systems (IPS) and potential systems. Then, we prove that the traffic flow model yields one nonlocal symmetry and hence we derive an exact solution for the given system. Moreover, we generate the conservation laws for the governing systems through the nonlinear self-adjoint property. Finally, we study the nonlinear behaviors like weak discontinuity ( C 1 -wave), characteristic shock for the physical model, and the impact of the anticipation factor on their evolutionary behavior graphically.