The KdV–Burgers equation in speed gradient viscous continuum model
The KdV–Burgers equation in speed gradient viscous continuum model
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DOI：
10.1016/j.physa.2011.10.014
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发表时间：
2012-02
影响因子：
3.3
通讯作者：
H. Ge;S. Lo
中科院分区：
文献类型：
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作者：
H. Ge;S. Lo
在微观二次速度差模型的基础上，提出了描述交通流的宏观模型——速度粘性连续体模型。将相对速度添加到运动方程中，这会导致连续介质模型中出现粘性效应。粘性连续介质模型克服了许多高阶连续介质模型中存在的向后传播问题。非线性分析表明，交通流中的密度波动会导致密度波。在不稳定开始时，一个小的扰动可能会导致由 Korteweg-de Vries-Burgers (KdV-Burgers) 方程描述的孤子，这在其他交通流模型中很少见，并且导出了孤子解。
Based on the microscopic two velocity difference model, a macroscopic model called speed viscous continuum model is developed to describe traffic flow. The relative velocities are added to the motion equation, which leads to viscous effects in continuum model. The viscous continuum model overcomes the backward travel problem, which exists in many higher-order continuum models. Nonlinear analysis shows that the density fluctuation in traffic flow leads to density waves. Near the onset of instability, a small disturbance could lead to solitons described by the Korteweg–de Vries–Burgers (KdV–Burgers) equation, which is seldom found in other traffic flow models, and the soliton solution is derived.