The time-dependent Ginzburg–Landau equation for the two-velocity difference model

doi:10.1088/1674-1056/20/8/080509

Abstract A thermodynamic theory is formulated to describe the phase transition and critical phenomenon in traffic flow. Based on the two-velocity difference model, the time-dependent Ginzburg—Landau (TDGL) equation under certain condition is derived to describe the traffic flow near the critical point through the nonlinear analytical method. The corresponding two solutions, the uniform and the kink solutions, are given. The coexisting curve, spinodal line and critical point are obtained by the first and second derivatives of the thermodynamic potential. The modified Korteweg de Vries (mKdV) equation around the critical point is derived by using the reductive perturbation method and its kink—antikink solution is also obtained. The relation between the TDGL equation and the mKdV equation is shown. The simulation result is consistent with the nonlinear analytical result.

Keywords: traffic flow two-velocity difference model TDGL equation mKdV equation

Received: 02 November 2010
Revised: 23 February 2011
Accepted manuscript online:

PACS:	05.70.Fh	(Phase transitions: general studies)
	05.70.Jk	(Critical point phenomena)

Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 11072117, 10802042, and 60904068), the Natural Science Foundation of Zhejiang Province of China (Grant No. Y6100023), the Natural Science Foundation of Ningbo City (Grant No. 2009B21003), and K. C. Wong Magna Fund in Ningbo University.

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Wu Shu-Zhen(吴淑贞), Cheng Rong-Jun(程荣军), and Ge Hong-Xia(葛红霞) The time-dependent Ginzburg–Landau equation for the two-velocity difference model 2011 Chin. Phys. B 20 080509

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The time-dependent Ginzburg–Landau equation for the two-velocity difference model

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