Asymptotic Dynamics of Ripples
  A new nonlinear equation governing asymptotic dynamics of ripples is derived by using a short wave perturbative expansion on a generalized version of the Green-Naghdi system. It admits peakon solutions with amplitude, velocity and width in interrelation and static compacton solutions with amplitude and width in interrelation. Short wave pattern formation is shown to result from a balance between linear dispersion and nonlinearity. 
M. A. Manna