The Korteweg-de Vires equation for the bidirectional pedestrian flow model considering the next-nearest-neighbor effect

This paper focuses on a two-dimensional bidirectional pedestrian flow model which involves the next-nearest-neighbor effect. The stability condition and the Korteweg-de Vries (KdV) equation are derived to describe the density wave of pedestrian congestion by linear stability and nonlinear analysis. Through theoretical analysis, the soliton solution is obtained.