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Journal of Applied Mathematics
Volume 2014, Article ID 539459, 7 pages
Research Article

The Burgers Equation for a New Continuum Model with Consideration of Driver’s Forecast Effect

1College of Automation, Northwestern Polytechnical University, Xi’an, Shaanxi 710129, China
2School of Science, Northwestern Polytechnical University, Xi’an, Shaanxi 710129, China

Received 18 June 2014; Revised 12 August 2014; Accepted 12 August 2014; Published 24 August 2014

Academic Editor: Weichao Sun

Copyright © 2014 Lei Yu and Bingchang Zhou. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A new continuum model with consideration of driver’s forecast effect is obtained to study the density wave problem and the stop-and-go phenomena. The stability condition of the new model is derived by using linear analysis. The triangular shock wave, one type of density wave, which is determined by Burgers equation in the stable region, is discussed in great detail with reductive perturbation method. The local cluster appears when we perform the numerical simulations for the new model. It also proves that the driver’s forecast effect has the positive effect of reducing the local cluster.