标题： 非局部时间演化方程与奇异积分及其在交通流模型中的应用 显示英文标题

标题： Non-local time evolution equation with singular integral and its application to traffic flow model

摘要： 我们考虑一个用于交通流的积分微分方程模型，这是Burgers方程模型的扩展。 为了讨论该模型，我们首先检查可积积分微分方程的一般设置，并发现它们是通过复域中可积方程的简单留数公式得到的。 作为该方法有效性的演示，我们列出了几个可积方程，包括一个带有双重奇异积分的差分方程和一个带有椭圆奇异积分的方程。 然后，我们讨论带有奇异积分的交通模型，并表明该模型在非局部性参数的作用下表现出自由流区域与拥堵区域之间的相互作用。 显示英文摘要

摘要： We consider an integro-differential equation model for traffic flow which is an extension of the Burgers equation model. To discuss the model, we first examine general settings for integrable integro-differential equations and find that they are obtained through a simple residue formula from integrable eqations in a complex domain. As demonstration of the efficiency of this approach, we list several integrable equations including a difference equation with double singular integral and an equation with elliptic singular integral. Then, we discuss the traffic model with singular integral and show that the model exhibits interaction between free flow region and congested region depending on the parameter of non-locality.