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

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.