Exact shock solution of a coupled system of delay differential equations: a car-following model

Details Exact shock solution of a coupled system of delay differential equations: a car-following model Exact shock solution of a coupled system of delay differential equations: a car-following model

2007-01-29

arxiv.org/abs/nlin/0701055v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

6 pages, 2 figures

Scientific paper

10.1143/JPSJ.76.083002

In this paper, we present exact shock solutions of a coupled system of delay differential equations, which was introduced as a traffic-flow model called {\it the car-following model}. We use the Hirota method, originally developed in order to solve soliton equations. %While, with a periodic boundary condition, this system has % a traveling-wave solution given by elliptic functions. The relevant delay differential equations have been known to allow exact solutions expressed by elliptic functions with a periodic boundary conditions. In the present work, however, shock solutions are obtained with open boundary, representing the stationary propagation of a traffic jam.

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