IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v357y2005i3p466-476.html
   My bibliography  Save this article

KdV and kink–antikink solitons in car-following models

Author

Listed:
  • Ge, H.X.
  • Cheng, R.J.
  • Dai, S.Q.

Abstract

The jams in the congested traffic are related with various density waves, which might be governed by the nonlinear wave equations, such as the Korteweg–de-Vries (KdV) equation, the Burgers equation and the modified Korteweg–de-Vries (mKdV) equation. Three different versions of optimal velocity models are examined. The stability conditions of the models are obtained by using the linear stability theory. The KdV equation near the neutral stability line and the mKdV equation around the critical point are derived by applying the reductive perturbation method, respectively. The traffic jams could be thus described by the KdV and kink–antikink soliton solutions for the two kinds of equations. The general solutions are given for, which can lead to specific solutions in previous work. Moreover, they are applied to solve a new model—the full velocity difference model and the corresponding KdV and kink–antikink soliton solutions could be quickly obtained, which demonstrates the general solutions presented herein are useful.

Suggested Citation

  • Ge, H.X. & Cheng, R.J. & Dai, S.Q., 2005. "KdV and kink–antikink solitons in car-following models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 357(3), pages 466-476.
    • Handle: RePEc:eee:phsmap:v:357:y:2005:i:3:p:466-476
    DOI: 10.1016/j.physa.2005.03.059
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437105003031
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2005.03.059?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Tu, Lihua & Zhou, Jie, 2019. "Memory’s effect on bidirectional pedestrian flow based on lattice hydrodynamic model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 534(C).
    2. Cheng, Qixiu & Liu, Zhiyuan & Lin, Yuqian & Zhou, Xuesong (Simon), 2021. "An s-shaped three-parameter (S3) traffic stream model with consistent car following relationship," Transportation Research Part B: Methodological, Elsevier, vol. 153(C), pages 246-271.
    3. Chen, Can & Cheng, Rongjun & Ge, Hongxia, 2019. "An extended car-following model considering driver’s sensory memory and the backward looking effect," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 278-289.
    4. Zhang, Jing & Wang, Bo & Li, Shubin & Sun, Tao & Wang, Tao, 2020. "Modeling and application analysis of car-following model with predictive headway variation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    5. Wang, Xiaoning & Liu, Minzhuang & Ci, Yusheng & Wu, Lina, 2022. "Effect of front two adjacent vehicles’ velocity information on car-following model construction and stability analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 607(C).
    6. Wang, Pengcheng & Yu, Guizhen & Wu, Xinkai & Qin, Hongmao & Wang, Yunpeng, 2018. "An extended car-following model to describe connected traffic dynamics under cyberattacks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 496(C), pages 351-370.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:357:y:2005:i:3:p:466-476. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.