The corona of the Sun is a unique environment in which magnetohydrodynamic (MHD) waves, one of the fundamental processes of plasma astrophysics, are open to a direct study. There is striking progress in both observational and theoretical research of MHD wave processes in the corona, with the main recent achievements summarized as follows: ▪ Both periods and wavelengths of the principal MHD modes of coronal plasma structures, such as kink, slow and sausage modes, are confidently resolved. ▪ Scalings of various parameters of detected waves and waveguiding plasma structures allow for the validation of theoretical models. In particular, kink oscillation period scales linearly with the length of the oscillating coronal loop, clearly indicating that they are eigenmodes of the loop. Damping of decaying kink and standing slow oscillations depends on the oscillation amplitudes, demonstrating the importance of nonlinear damping. ▪ The dominant excitation mechanism for decaying kink oscillations is associated with magnetized plasma eruptions. Propagating slow waves are caused by the leakage of chromospheric oscillations. Fast wave trains could be formed by waveguide dispersion. ▪ The knowledge gained in the study of coronal MHD waves provides ground for seismological probing of coronal plasma parameters, such as the Alfvén speed, the magnetic field and its topology, stratification, temperature, fine structuring, polytropic index, and transport coefficients.

Astronomy & Astrophysics (A&A) is an international journal which publishes papers on all aspects of astronomy and astrophysics

The concept of a new form of solitary waves-super solitary waves-is proposed, specific for embracing one or several interior separatrices on their wave phase portraits. The super solitary waves of an ion-acoustic type exist, for example, in nonmagnetized plasma containing five species of charged particles. For such plasma, electrostatic potential for ion-acoustic super solitary waves is calculated. The super solitary waves can be easily identified among usual solitons, e.g., in differential circuits installed into the measuring channel.