Abstract
On a gradient road gravity as an external force acts upon running vehicles which show different characteristics from those on normal road. We investigated traffic flow on a gradient with a consideration of speed difference effect analytically and numerically. Stability and instability conditions were obtained by the use of linear stability theory. Nonlinear analysis method was taken to derive the mKdV equation and its kink-antikink soliton solution was obtained near the critical point in the unstable region. Kink-antikink density waves were reproduced in the simulation with a variable slope. Results show that the slope effect plays an important role in traffic flow.
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