Journal
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
Volume 389, Issue 14, Pages 2825-2834Publisher
ELSEVIER
DOI: 10.1016/j.physa.2010.03.007
Keywords
Traffic flow; Lattice hydrodynamic model; KdV equation; mKdV equation; Numerical simulation
Categories
Funding
- National Basic Research Program of China [2006CB705500]
- National Natural Science Foundation of China [10532060, 10602025, 10802042]
- Natural Science Foundation of Ningbo [2009A610154, 2009A610014]
- Ningbo University
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The lattice hydrodynamic model is not only a simplified version of the macroscopic hydrodynamic model, but also connected with the microscopic car following model closely. The modified Korteweg-de Vries (mKdV) equation related to the density wave in a congested traffic region has been derived near the critical point since Nagatani first proposed it. But the Korteweg-de Vries (KdV) equation near the neutral stability line has not been studied, which has been investigated in detail for the car following model. We devote ourselves to obtaining the KdV equation from the original lattice hydrodynamic models and the KdV soliton solution to describe the traffic jam. Especially, we obtain the general soliton solution of the KdV equation and the mKdV equation. We review several lattice hydrodynamic models, which were proposed recently. We compare the modified models and carry out some analysis. Numerical simulations are conducted to demonstrate the nonlinear analysis results. (C) 2010 Elsevier B.V. All rights reserved.
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