The time-dependent Ginzburg-Landau equation for the two-velocity difference model |
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Authors: | Wu Shu-Zhen Cheng Rong-Jun and Ge Hong-Xia |
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Institution: | Faculty of Science, Ningbo University, Ningbo 315211, China;Department of Fundamental Course, Ningbo Institute of Technology, Zhejiang University, Ningbo 315100, China;Faculty of Science, Ningbo University, Ningbo 315211, China |
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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. |
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Keywords: | traffic flow two-velocity difference model TDGL equation mKdV equation |
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