Abstract
The weakly nonlinear standing waves on the surface of a self-gravitating incompressible fluid column are investigated in the presence of, a uniform axial-magnetic field. By use of the method of multiple scales, we have shown that near the critical wave number, the amplitude modulation of a standing wave can be described by a nonlinear Schrodinger equation with the roles of time and space variable interchanged. It is demonstrated that in presence of a magnetic field, the system is always stable near the critical wave number.
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