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Applied Mathematics and Mechanics (English Edition) ›› 2014, Vol. 35 ›› Issue (2): 167-176.doi: https://doi.org/10.1007/s10483-014-1781-x

• 论文 • 上一篇    下一篇

Solitary wave solutions to higher-order traffic flow model with large diffusion

菅肖霞1,4 张鹏1,4  S. C. WONG2  乔殿梁1,4 崔岐柱3   

  1. 1. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, P. R. China;
    2. Department of Civil Engineering, The University of Hong Kong, Pokfulam Road, Hong Kong, P. R. China;
    3. Department of Transportation Engineering, TOD-based Sustainable Urban Transportation Center, Ajou University, Suwon 443-749, Korea;
    4. Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai 200072, P. R. China
  • 收稿日期:2013-03-07 修回日期:2013-07-08 出版日期:2014-02-27 发布日期:2014-02-18

Solitary wave solutions to higher-order traffic flow model with large diffusion

 JIAN Xiao-Xia1,4, ZHANG Peng1,4,  S. C. WONG2,  QIAO Dian-Liang1,4, CUI Qi-Zhu3   

  1. 1. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, P. R. China;
    2. Department of Civil Engineering, The University of Hong Kong, Pokfulam Road, Hong Kong, P. R. China;
    3. Department of Transportation Engineering, TOD-based Sustainable Urban Transportation Center, Ajou University, Suwon 443-749, Korea;
    4. Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai 200072, P. R. China
  • Received:2013-03-07 Revised:2013-07-08 Online:2014-02-27 Published:2014-02-18

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摘要： This paper uses the Taylor expansion to seek an approximate Kortewegde Vries equation (KdV) solution to a higher-order traffic flow model with sufficiently large diffusion. It demonstrates the validity of the approximate KdV solution considering all the related parameters to ensure the physical boundedness and the stability of the solution. Moreover, when the viscosity coefficient depends on the density and velocity of the flow, the wave speed of the KdV solution is naturally related to either the first or the second characteristic field. The finite element method is extended to solve the model and examine the stability and accuracy of the approximate KdV solution.

关键词: 电报方程组, 不动点定理, 双周期解, 锥, higher-order traffic flow model, viscosity coefficient, approximate Kortewegde Vries equation (KdV) solution, finite element scheme

Abstract: This paper uses the Taylor expansion to seek an approximate Kortewegde Vries equation (KdV) solution to a higher-order traffic flow model with sufficiently large diffusion. It demonstrates the validity of the approximate KdV solution considering all the related parameters to ensure the physical boundedness and the stability of the solution. Moreover, when the viscosity coefficient depends on the density and velocity of the flow, the wave speed of the KdV solution is naturally related to either the first or the second characteristic field. The finite element method is extended to solve the model and
examine the stability and accuracy of the approximate KdV solution.

Key words: cone, telegraph system, fixed point theorem, higher-order traffic flow model, viscosity coefficient, approximate Kortewegde Vries equation (KdV) solution, finite element scheme, doubly periodic solution

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