[en] The evolution of two dimensional wave packets on the surface of a self-gravitating fluid layer is investigated and shown to be governed by a nonlinear Schroedinger equation. The wave train of finite amplitude is modulationally unstable. Obtained also are the dynamical equations for the second harmonic resonance. The analysis reveals that the general motion consists of both amplitude and phase modulated waves of which the pure phase and amplitude modulated waves, solitary waves, and phase jump are just the special cases. (orig.)