Abstract
The radial modes of the coronal loops are used to interpret the observed microwave and hard x-ray pulsations during flares. The properties of radial oscillations are well studied in the approximation of linear magnetohydrodynamics, and their further study requires a nonlinear approach. Obviously, the first step in this path is the weakly nonlinear approximation, which is used in this work. The study uses cylindrical geometry with the previously obtained nonlinear Schrodinger equation for the amplitude of radial oscillations. The conditions under which modulation instability of radial modes takes place, leading to the appearance of quasiperiodic oscillations, are studied.
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