Nonlinear dispersive waves on the surface of a self-gravitating fluid layer

Astronomy and Astrophysics – Astrophysics

Scientific paper

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Celestial Bodies, Incompressible Fluids, Inviscid Flow, Surface Waves, Wave Dispersion, Wave Packets, Linear Equations, Nonlinear Equations, Phase Modulation, Resonance, Schroedinger Equation, Solitary Waves, Steady State

Scientific paper

The evolution of two-dimensional wave packets on the surface of a self-gravitating fluid layer is studied and shown to be governed by a nonlinear Schroedinger equation. The wave train of finite amplitude is found to be modulationally unstable. Also obtained are the dynamical equations for the second harmonic resonance. The analysis shows 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.

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