Abstract
The propagation of nonlinear hydromagnetic waves in a highly conducting, self-gravitating fluid in a cylindrical geometry, subject to the convective forces produced by a radial temperature gradient, is treated in a Boussinesq approximation. Exact wave solutions of the nonlinear magnetohydrodynamic equations (in the Boussinesq approximation) in the presence of convective forces are obtained for the case when the physical quantities are independent of the axial coordinate or the azimuthal angle in the cylindrical coordinates. The solutions represent waves propagating in the azimuthal or axial direction under the influence of the helical magnetic and velocity fields and the convective forces. The solutions may be applicable to the hydromagnetic waves in the Earth's fluid core and the solar convection zone.
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