Nonlinear dispersive shallow water equationsfor a non-stationary bottom
A uniform derivation of the Green-Naghdi, Zheleznyak-Pelinovsky and Aleshkov nonlinear dispersive equations describing water surface waves is given for the case of a non-stationary bottom profile. It is shown, that the Green-Naghdi's and Zheleznyak- Pelinovsky's equations are just different forms of the second order approximation for the system of shallow water equations which accounts for a bottom deformation and movement.