Are galactic magnetohydrodynamic waves coupled?

Recently, Fan & Lou considered the excitation and time evolution of hydromagnetic density waves in a differentially rotating thin gaseous disc embedded in an azimuthal magnetic field. The authors found that both fast and slow hydromagnetic density waves are amplified while they ‘swing’ from leading to trailing configurations, and gave a detailed description of the phenomenon. Fan & Lou noticed that the results of their numerical study indicate the existence of a ‘coupling’ between slow and fast waves. In this Letter we prove, in a simple and exact analytic way, that the coupling between slow and fast waves, presumed by Fan & Lou on the basis of their numerical study, indeed exists. We show that the coupling is induced exclusively by the presence of the velocity shear in the gaseous disc, and that it leads to the mutual transformations of the different density wave modes. We argue that the shear-induced wave transformations may play a significant role in the overall dynamics of galactic MHD density waves.