Muramatsu M, Nagatani T
Division of Thermal Science, College of Engineering, Shizuoka University, Hamamatsu 432-8561, Japan.
Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 1999 Jul;60(1):180-7. doi: 10.1103/physreve.60.180.
Soliton density wave is investigated numerically and analytically in the optimal velocity model (a car-following model) of a one-dimensional traffic flow with open boundaries. Soliton density wave is distinguished from the kink density wave. It is shown that the soliton density wave appears only at the threshold of occurrence of traffic jams. The Korteweg-de Vries (KdV) equation is derived from the optimal velocity model by the use of the nonlinear analysis. It is found that the traffic soliton appears only near the neutral stability line. The soliton solution is analytically obtained from the perturbed KdV equation. It is shown that the soliton solution obtained from the nonlinear analysis is consistent with that of the numerical simulation.
在具有开放边界的一维交通流的最优速度模型（一种跟驰模型）中，对孤子密度波进行了数值和解析研究。孤子密度波与扭结密度波不同。结果表明，孤子密度波仅出现在交通拥堵发生的阈值处。通过非线性分析从最优速度模型推导出了科特韦格 - 德弗里斯（KdV）方程。发现交通孤子仅出现在中性稳定线附近。从微扰KdV方程解析得到了孤子解。结果表明，从非线性分析得到的孤子解与数值模拟结果一致。
