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The KdV–Burgers equation in speed gradient viscous continuum model

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  • Ge, Hong-Xia
  • Lo, Siu-ming

Abstract

Based on the microscopic two velocity difference model, a macroscopic model called speed viscous continuum model is developed to describe traffic flow. The relative velocities are added to the motion equation, which leads to viscous effects in continuum model. The viscous continuum model overcomes the backward travel problem, which exists in many higher-order continuum models. Nonlinear analysis shows that the density fluctuation in traffic flow leads to density waves. Near the onset of instability, a small disturbance could lead to solitons described by the Korteweg–de Vries–Burgers (KdV–Burgers) equation, which is seldom found in other traffic flow models, and the soliton solution is derived.

Suggested Citation

  • Ge, Hong-Xia & Lo, Siu-ming, 2012. "The KdV–Burgers equation in speed gradient viscous continuum model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(4), pages 1652-1656.
    • Handle: RePEc:eee:phsmap:v:391:y:2012:i:4:p:1652-1656
    DOI: 10.1016/j.physa.2011.10.014
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    Cited by:

    1. Jafaripournimchahi, Ammar & Cai, Yingfeng & Wang, Hai & Sun, Lu & Yang, Biao, 2022. "Stability analysis of delayed-feedback control effect in the continuum traffic flow of autonomous vehicles without V2I communication," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 605(C).
    2. Li, Chuan-Yao & Huang, Hai-Jun & Tang, Tie-Qiao, 2017. "Analysis of user equilibrium for staggered shifts in a single-entry traffic corridor with no late arrivals," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 474(C), pages 8-18.

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