The Applications Of The Korteweg-de Vires Equation For Pedestrian Flow

Assemblies for rally, march, and escape always causes serious stampedes. That arousedscholars’ highly attentions gradually. According to studies, scholars’ have found pedestrianfow is similar to trafc fow. Based on new models proposed recently for pedestrian fow, thecorresponding nonlinear analysis theoretical analysis are present. The KdV equation near theneutral stability line is derived to describe pedestrian jam.The thesis is arranged as follows:Ⅰ.The Korteweg-de Vires equation for the bidirectional pedestrian fow model consideringthe next-nearest-neighbor efect. Based on the extended lattice hydrodynamic pedestrian mod-el taking the interaction of the next-nearest-neighbor persons into account which is proposedby Wen.et.al., the Korteweg-de-Vries(KdV) equation is gotten near the neutral stability linethrough the nonlinear analysis method. The soliton solution is derivedⅡ.The Korteweg-de Vires equation for the bidirectional pedestrian fow model with theefect of drag coefcient. In the light of the one-dimensional lattice hydrodynamic model pro-posed by Nagatani before, Zhang established he bidirectional pedestrian fow model with theefect of drag coefcient. Then, the linear stability theory is used to obtain the neutral stabilitycondition. The KdV equation around the neutral stability line is conducted and the solitonsolution is obtained.Ⅲ.The Korteweg-de Vires equation for the lattice model for bidirectional pedestrian fow ongradient road. Recently, Zhu et al. presented a lattice hydrodynamic model for trafc fow witha consideration of slope road. Then, Zhang established the bidirectional pedestrian fow modelon gradient road. The KdV equation and the soliton solution around the neutral stability lineis obtained.