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Propagation of three dimensional magnetosonic waves is considered for ahomogeneous shear flow of an incompressible fluid. The analytical solutions forall magnetohydrodynamic variables are presented by confluent Heun functions.The problem is reduced to finding a solution of an effective Schroedingerequation. The amplification of slow magnetosonic waves is analyzed in greatdetails. A simple formula for the amplification coefficient is derived. Thevelocity shear primarily affects the incompressible limit of slow magnetosonicwaves. The amplification is very strong for slow magnetosonic waves in thelong-wavelength limit. It is demonstrated that the amplification of those wavesleads to amplification of turbulence. The phenomenology of Shakura-Sunyaev forthe friction in accretion disks is derived in the framework of the Kolmogorovturbulence. The presented findings may be the key to explaining the anomalousplasma heating responsible for the luminosity of quasars. It is suggested thatwave amplification is the keystone of the self-sustained turbulence inaccretion disks.

Amplification of Slow Magnetosonic Waves by Shear Flow: Heating and Friction Mechanisms of Accretion Disks