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

doi:10.1088/1674-1056/19/10/100512

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.

Keywords: traffic flow lattice hydrodynamic model mKdV equation

Received: 22 January 2010
Revised: 12 April 2010
Accepted manuscript online:

PACS:	05.45.Yv	(Solitons)
	05.50.+q	(Lattice theory and statistics)

Fund: 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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Yu Han-Mei(余寒梅), Cheng Rong-Jun(程荣军), and Ge Hong-Xia(葛红霞) General solution of the modified Korteweg-de-Vries equation in the lattice hydrodynamic model 2010 Chin. Phys. B 19 100512

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

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