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.