中国物理B ›› 2008, Vol. 17 ›› Issue (1): 23-26.doi: 10.1088/1674-1056/17/1/004

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The density wave in a new anisotropic continuum model

葛红霞1, 戴世强2, 董力耘2   

  1. (1)College of Sciences, Ningbo University, Ningbo 315211, China;Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China; (2)Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China
  • 出版日期:2008-01-20 发布日期:2008-01-20
  • 基金资助:
    Project supported by the National Basic Research Program of China (Grant No 2006CB705500), the National Natural Science Foundation of China (Grant Nos 10532060 and 10602025), Scientific Research Fund of Zhejiang Provincial Education Department, China (Gra

The density wave in a new anisotropic continuum model

Ge Hong-Xia(葛红霞)a)b), Dai Shi-Qiang(戴世强)b)†, and Dong Li-Yun(董力耘)b)   

  1. a College of Sciences, Ningbo University, Ningbo 315211, China; b Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China
  • Online:2008-01-20 Published:2008-01-20
  • Supported by:
    Project supported by the National Basic Research Program of China (Grant No 2006CB705500), the National Natural Science Foundation of China (Grant Nos 10532060 and 10602025), Scientific Research Fund of Zhejiang Provincial Education Department, China (Gra

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摘要： In this paper the new continuum traffic flow model proposed by Jiang {\it et al is developed based on an improved car-following model, in which the speed gradient term replaces the density gradient term in the equation of motion. It overcomes the wrong-way travel which exists in many high-order continuum models. Based on the continuum version of car-following model, the condition for stable traffic flow is derived. Nonlinear analysis shows that the density fluctuation in traffic flow induces a variety of density waves. Near the onset of instability, a small disturbance could lead to solitons determined by the Korteweg--de-Vries (KdV) equation, and the soliton solution is derived.

关键词: high-order continuum model, density waves, KdV equation

Abstract: In this paper the new continuum traffic flow model proposed by Jiang et al is developed based on an improved car-following model, in which the speed gradient term replaces the density gradient term in the equation of motion. It overcomes the wrong-way travel which exists in many high-order continuum models. Based on the continuum version of car-following model, the condition for stable traffic flow is derived. Nonlinear analysis shows that the density fluctuation in traffic flow induces a variety of density waves. Near the onset of instability, a small disturbance could lead to solitons determined by the Korteweg--de-Vries (KdV) equation, and the soliton solution is derived.

Key words: high-order continuum model, density waves, KdV equation

中图分类号:  (Granular models of complex systems; traffic flow)

  • 45.70.Vn
05.45.Yv (Solitons) 02.30.Jr (Partial differential equations)