Exact Traveling Cluster Solutions of Differential Equations with Delay for a Traffic Flow Model

  • K. Hasebe
  • A. Nakayama
  • Y. Sugiyama
Conference paper


Exact solutions of the first order differential equation with delay are derived. The equation has been introduced as a model of traffic flow. The solution describes the traveling cluster of jam, which is characterized by Jacobi’s elliptic function. The system is related to some soliton systems.


Traffic Flow Travel Wave Solution Elliptic Function Order Differential Equation Granular Flow 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    D.E. Wolf, M. Schreckenberg, and A. Bachem, (Eds.), Traffic and Granular Flow, (World Scientific, Singapore, 1996);Google Scholar
  2. 1b.
    M. Schreckenberg and D.E. Wolf, (Eds.), Traffic and Granular Flow ’97, (Springer Verlag, Singapore, 1998).Google Scholar
  3. 2.
    G.F. Newell, Oper. Res. 9, 2209 (1961).MathSciNetCrossRefGoogle Scholar
  4. 3.
    G.B. Whitham, Proc. R. Soc. Lond. A 428, 49 (1990).MathSciNetMATHCrossRefGoogle Scholar
  5. 4.
    M. Bando, K. Hasebe, A. Nakayama, A. Shibata, and Y. Sugiyama, Phys. Rev. E 51, 1035 (1995).CrossRefGoogle Scholar
  6. 4b.
    M. Bando, K. Hasebe, A. Nakayama, A. Shibata, and Y. Sugiyama,Japan J. of Ind. and Appl. Math. 11, 203 (1994), Y. Sugiyama, in [1].MathSciNetMATHCrossRefGoogle Scholar
  7. 5.
    K. Hasebe, A. Nakayama, and Y. Suigiyama, Phys. Lett. A 259, 135 (1999).MathSciNetMATHCrossRefGoogle Scholar
  8. 6.
    Y. Igarashi, K. Itoh, and K. Nakanishi, J. Phys. Soc. Japan 68, 791 (1999).MathSciNetMATHCrossRefGoogle Scholar
  9. 7.
    M.J. Ablowitz and J.F. Ladik, J. Math. Phys. 17, 1011 (1976).MathSciNetMATHCrossRefGoogle Scholar
  10. 8.
    M. Wadati, Prog. Theor. Phys. Suppl. 59, 36 (1976).CrossRefGoogle Scholar
  11. 9.
    R. Hirota and J. Satsuma, Prog. Theor. Phys. Suppl. 59, 64 (1976).MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • K. Hasebe
    • 1
  • A. Nakayama
    • 2
  • Y. Sugiyama
    • 3
  1. 1.Faculty of Business AdministrationAichi UniversityMiyoshiJapan
  2. 2.Gifu Keizai UniversityOhgakiJapan
  3. 3.Division of Mathematical ScienceCity College of MieTsuJapan

Personalised recommendations