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This article deals with the characteristic of the multiple velocity difference car-following model. We obtain the stability conditions of the model by using the linear stability analysis, and find that the stable region is apparently enlarged by adjusting the information about the multi-velocity difference. We study the nonlinear characteristics of the model by applying the reductive perturbation method. We obtain the Burgers equation and the modified Korteweg-de-Vries (mKdV) equation around the critical point and the Korteweg-de-Vries (KdV) equation near the neutral stability line in the stable region and the unstable region and the metastable region. The soliton solution of Burgers equation, the kink-antikink solution of mKdV equation, and the solition solution of KdV equation describe the traffic jams.
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Keywords:
- multi-velocity difference car-following model /
- Burgers equation /
- mKdV equation /
- KdV equation
[1] Komatsu T, Sasa S 1995 Phys. Rev. E 52 5574
[2] Ge H X, Cheng R J, Dai S Q 2005 Physica A 357 466
[3] Xue Y 2002 Ph. D. Dissertation (Shanghai: Shanghai University) (in Chinese) [薛郁 2002 博士学位论文 (上海:上海大学)]
[4] Tang T Q, Huang H J, Wong S C, Jiang R 2009 Chin. Phys. B 18 975
[5] Tian J F, Jia B, Li X G, Gao Z Y 2010 Chin. Phys. B 19 197
[6] Peng G H, Sun D H, He H P 2008 Acta Phys. Sin. 57 7541 (in Chinese) [彭光含, 孙棣华, 何恒攀 2008 物理学报 57 7541]
[7] Peng G H 2009 J. Sichuan Univ. (Natural Science Edition) 46 1057 [彭光含 2009 四川大学学报 (自然科学版) 46 1057]
[8] Peng G H 2010 Chin. Phys. B 19 056401
[9] Peng G H, Sun D H 2009 Chin. Phys. B 18 5420
[10] Xue Y 2002 Chin. Phys. B 11 1128
[11] Nagatani T 1999 Phys. Rev. E 60 6395
[12] Wang T, Gao Z Y, Zhao X M 2006 Acta Phys. Sin. 55 634 (in Chinese) [王涛, 高自友, 赵小梅 2006 物理学报 55 634]
[13] Pipes L A 1953 J. Appl. Phys. 24 274
[14] Newell G F 1961 Oper. Res. 9 209
[15] Bando M, Hasebe K, Nakyaama A, Sugiyama Y 1995 Phys. Rev. E 51 1035
[16] Jiang R, Wu Q S, Zhu Z J 2000 Chin. Sci. Bull. 45 1895 (in chinese)[姜锐, 吴清松, 朱祚金 2000 科学通报 45 1895]
[17] Nayfeh A H 1981 Introduction to Perturbation Technique (New York: Wiley) p325
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[1] Komatsu T, Sasa S 1995 Phys. Rev. E 52 5574
[2] Ge H X, Cheng R J, Dai S Q 2005 Physica A 357 466
[3] Xue Y 2002 Ph. D. Dissertation (Shanghai: Shanghai University) (in Chinese) [薛郁 2002 博士学位论文 (上海:上海大学)]
[4] Tang T Q, Huang H J, Wong S C, Jiang R 2009 Chin. Phys. B 18 975
[5] Tian J F, Jia B, Li X G, Gao Z Y 2010 Chin. Phys. B 19 197
[6] Peng G H, Sun D H, He H P 2008 Acta Phys. Sin. 57 7541 (in Chinese) [彭光含, 孙棣华, 何恒攀 2008 物理学报 57 7541]
[7] Peng G H 2009 J. Sichuan Univ. (Natural Science Edition) 46 1057 [彭光含 2009 四川大学学报 (自然科学版) 46 1057]
[8] Peng G H 2010 Chin. Phys. B 19 056401
[9] Peng G H, Sun D H 2009 Chin. Phys. B 18 5420
[10] Xue Y 2002 Chin. Phys. B 11 1128
[11] Nagatani T 1999 Phys. Rev. E 60 6395
[12] Wang T, Gao Z Y, Zhao X M 2006 Acta Phys. Sin. 55 634 (in Chinese) [王涛, 高自友, 赵小梅 2006 物理学报 55 634]
[13] Pipes L A 1953 J. Appl. Phys. 24 274
[14] Newell G F 1961 Oper. Res. 9 209
[15] Bando M, Hasebe K, Nakyaama A, Sugiyama Y 1995 Phys. Rev. E 51 1035
[16] Jiang R, Wu Q S, Zhu Z J 2000 Chin. Sci. Bull. 45 1895 (in chinese)[姜锐, 吴清松, 朱祚金 2000 科学通报 45 1895]
[17] Nayfeh A H 1981 Introduction to Perturbation Technique (New York: Wiley) p325
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