Traveling wave solution of higher-order traffic flow model with discontinuous fundamental diagram

The traveling wave solution of a unified higher-order traffic flow model is investigated with a discontinuous fundamental diagram under the Lagrange coordinate. The equilibrium velocity is a piecewise function which consists of two concave functions. The weak solution theory is applied to study the traveling wave solution of the model, in which a set of equations about the characteristic parameters are obtained. Through numerical simulation, the moving cluster solutions of the anisotropic and isotropic traffic flow models are reproduced, respectively. The numerical results agree with the analytical ones.