Gravity waves in a magnetized shear layer

We use the equations governing the propagation of a gravity wave in the presence of a background flow and magnetic field to derive, in the Boussinesq approximation, dispersion relations for plane wave solutions in certain special cases. We show how, under conditions typical of the interior of the Sun, the addition of a magnetic field may prevent certain wavevectors from propagating and alter the existence and position of any critical layer that might absorb the gravity wave.