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Research Papers

# KdV and Kink-Antikink Solitons in an Extended Car-Following Model

[+] Author and Article Information
Yanfei Jin

Department of Mechanics, Beijing Institute of Technology, 100081 Beijing, Chinayanfeijin@nuaa.edu.cn

Meng Xu, Ziyou Gao

State Key Laboratory of Rail Traffic Control and Safety, Beijing Jiaotong University, 100044 Beijing, China

J. Comput. Nonlinear Dynam 6(1), 011018 (Oct 13, 2010) (7 pages) doi:10.1115/1.4002336 History: Received July 29, 2009; Revised September 22, 2009; Published October 13, 2010; Online October 13, 2010

## Abstract

An extended car-following model is proposed in this paper by using the generalized optimal velocity function and considering the multivelocity differences. The stability condition of the model is derived by using the linear stability theory. From the reductive perturbation method and nonlinear analysis, the Korteweg–de Vries (KdV) and modified Korteweg–de Vries (mKdV) equations are derived to describe the traffic behaviors near the neutral stability line and around the critical point, respectively. The corresponding soliton wave and kink-antikink soliton solution are used to describe the different traffic jams. It is found that the generalized optimal velocity function and multivelocity differences consideration can further stabilize traffic flow and suppress traffic jams. The theoretical results are well verified through numerical simulations.

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## Figures

Figure 1

Neutral stability lines in the headway-sensitivity space for vmax=2.0, hc=4.0, and λ=0.5 with (a) different values of α, p=0.2 and (b) different values of p, α=0.2

Figure 2

Phase diagrams in the headway-sensitivity space for vmax=2.0, hc=4.0, and λ=0.5: (a) with different α, p=0.2 and (b) different values of p, α=0.2; the solid lines represent the coexisting curves and the dotted lines represent the neutral stability curve (spinodal line)

Figure 3

Space-time evolution of the headway with different p for a=0.6, α=0.1, and λ=0.5 after t=5000

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