Nonlinear disturbances in self-gravitating media

Using a multiple time-scale method, the weakly nonlinear waves on a self-gravitating incompressible fluid column are investigated. The analysis reveals that near the wavenumber k = ksub(c), the amplitude modulation of a standing wave can be described by the nonlinear Schroedinger equation with the roles of time and space variables interchanged. The nonlinear cutoff wavenumber, which depends sensitively on initial conditions, can be derived from nonlinear Schroedinger equation so obtained. The finite amplitude standing wave is stable against modulation. (orig.)