Wu, Chun-xiu; Zhang, Peng; Wong, S. C.; Qiao, Dian-liang; Dai, Shi-qiang Solitary wave solution to Aw-Rascle viscous model of traffic flow. (English) Zbl 1400.35200 Appl. Math. Mech., Engl. Ed. 34, No. 4, 523-528 (2013). Summary: A traveling wave solution to the Aw-Rascle traffic flow model that includes the relaxation and diffusion terms is investigated. The model can be approximated by the well-known Kortweg-de Vries (KdV) equation. A numerical simulation is conducted by the first-order accurate Lax-Friedrichs scheme, which is known for its ability to capture the entropy solution to hyperbolic conservation laws. Periodic boundary conditions are applied to simulate a lengthy propagation, where the profile of the derived KdV solution is taken as the initial condition to observe the change of the profile. The simulation shows good agreement between the approximated KdV solution and the numerical solution. Cited in 6 Documents MSC: 35Q35 PDEs in connection with fluid mechanics 35C07 Traveling wave solutions 65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs 35C08 Soliton solutions 35L65 Hyperbolic conservation laws 35Q53 KdV equations (Korteweg-de Vries equations) Keywords:hyperbolic conservation law; higher-order traffic flow model; traveling wave solution; conservative scheme PDFBibTeX XMLCite \textit{C.-x. Wu} et al., Appl. Math. Mech., Engl. 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