含智能提示限速的全速度差模型的稳定性和孤立波  

Stability and solitary waves of the full velocity difference model with intelligent prompt speed limit

作　　者：曹芳 化存才[1] CAO Fang;HUA Cun-cai(School of Mathematics,Yunnan Normal University,Kunming 650500,China)

机构地区：[1]云南师范大学数学学院,云南昆明650500

出　　处：《云南民族大学学报（自然科学版）》2020年第4期338-343,共6页Journal of Yunnan Minzu University:Natural Sciences Edition

基　　金：国家自然科学基金(11162020).

摘　　要：给出了含智能提示限速信息的速度差模型.通过稳定性分析导出了模型的稳定性条件,结果表明智能限速信息提示扩大了交通流的稳定区域,并对稳定性条件进行了3种精准分析.通过约化摄动方法在稳定区域导出Burgers方程,并给出其孤立波;在亚稳定区域内导出KdV方程,并给出其孤立波;在不稳定区域,导出mKdV方程,并给出其扭结-反扭结波解.根据孤立波解对交通流进行了相应的阐释.This paper presents a velocity difference model with intelligently reminded speed limit information. Through the stability analysis, the stability conditions of the model are derived. The results show that the intelligent speed limit information prompt expands the stability region of the traffic flow. The stability condition is analyzed precisely in three cases. Through the reduced perturbation method, Burgers equation in the stable region is derived and its solitary wave is given. KdV equation in the metastable region is derived and its solitary wave is given. mKDV equation in the unstable region is derived and its kink-anti-kink solutions are given. The traffic flow is explained according to the obtained solitary waves.

关 键 词：智能交通 限速提示 约化摄动法 速度差模型 孤立波 

分 类 号：U491[交通运输工程—交通运输规划与管理]