Dynamics of solitary waves over an erodible surface

In this paper, we propose a new approach in the study of the dynamics of solitary waves over an erodible surface consisting of non-cohesive particles transported by a constant unidirectional fluid. Using the multiple scale perturbation method, we show that the system can be described by the Kadomtsev–Petviashvili equation. The solution presented here shows that this mathematical model can be used to explain the dynamical behaviour of sand dunes in the desert.