Alfvén-Magnetosonic Waves Interaction
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The nonlinear propagation of the Alfvén and magnetosonic waves in the solar corona is investigated in terms of model equations. Due to viscous effects taken into account the propagation of the Alfvén wave itself is governed by a Burgers-type equation. The Alfvén waves exhibit a tendency to drive both the slow and fast magnetosonic waves. For this process model equations are a generalization of the Zakharov equations. The propagation of the magnetosonic waves is described by linearized Boussinesq-type equations with ponderomotive terms due to the Alfvén wave. Both long and short Alfvén waves are considered. Also the limits of the slow and fast modes are investigated. An approximate shock wave solution has been found for a vertically propagating slow mode. Numerical results for the fast mode propagating perpendicular to the magnetic field show the effect of inhomogeneity and pumping on a shock as the solution of the homogeneous Burgers equation.
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