中国物理B ›› 2010, Vol. 19 ›› Issue (10): 100512-100512.doi: 10.1088/1674-1056/19/10/100512

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General solution of the modified Korteweg-de-Vries equation in the lattice hydrodynamic model

程荣军1, 余寒梅2, 葛红霞2   

  1. (1)Department of Fundamental Course, Ningbo Institute of Technology, Zhejiang University, Ningbo 315100, China; (2)Faculty of Science, Ningbo University, Ningbo 315211, China
  • 收稿日期:2010-01-22 修回日期:2010-04-12 出版日期:2010-10-15 发布日期:2010-10-15
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant Nos. 10602025, 10532060 and 60904068), the National Basic Research Program of China (Grant No. 2006CB705500), the Natural Science Foundation of Ningbo City (Grant Nos. 2009B21003, 2009A610154, 2009A610014) and K.C. Wong Magna Fund in Ningbo University.

General solution of the modified Korteweg-de-Vries equation in the lattice hydrodynamic model

Yu Han-Mei(余寒梅)a), Cheng Rong-Jun(程荣军)b), and Ge Hong-Xia(葛红霞)a)†ger   

  1. a Faculty of Science, Ningbo University, Ningbo 315211, China; b Department of Fundamental Course, Ningbo Institute of Technology, Zhejiang University, Ningbo 315100, China
  • Received:2010-01-22 Revised:2010-04-12 Online:2010-10-15 Published:2010-10-15
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant Nos. 10602025, 10532060 and 60904068), the National Basic Research Program of China (Grant No. 2006CB705500), the Natural Science Foundation of Ningbo City (Grant Nos. 2009B21003, 2009A610154, 2009A610014) and K.C. Wong Magna Fund in Ningbo University.

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摘要： Traffic congestion is related to various density waves, which might be described by the nonlinear wave equations, such as the Burgers, Korteweg-de-Vries (KdV) and modified Korteweg-de-Vries (mKdV) equations. In this paper, the mKdV equations of four different versions of lattice hydrodynamic models, which describe the kink--antikink soliton waves are derived by nonlinear analysis. Furthermore, the general solution is given, which is applied to solving a new model --- the lattice hydrodynamic model with bidirectional pedestrian flow. The result shows that this general solution is consistent with that given by previous work.

Abstract: Traffic congestion is related to various density waves, which might be described by the nonlinear wave equations, such as the Burgers, Korteweg-de-Vries (KdV) and modified Korteweg-de-Vries (mKdV) equations. In this paper, the mKdV equations of four different versions of lattice hydrodynamic models, which describe the kink–antikink soliton waves are derived by nonlinear analysis. Furthermore, the general solution is given, which is applied to solving a new model —— the lattice hydrodynamic model with bidirectional pedestrian flow. The result shows that this general solution is consistent with that given by previous work.

Key words: traffic flow, lattice hydrodynamic model, mKdV equation

中图分类号:  (Solitons)

  • 05.45.Yv
05.50.+q (Lattice theory and statistics)