The Stability of the Relativistic Alfvén Waves

Within the framework of the special relativity, the system of reference comoving with Alfvén wave is defined and the form of the perturbations with respect to this system are deduced. The system of equations corresponding to the interaction of the waves, in the case when the relativistic Alfvén wave can generate new Alfvén waves and magnetosonic waves, is obtained in the most general form. In the one‐dimensional case the time dependent perturbation method is used for obtain the dispersion equation for the relativistic coupled waves (decay processes). Finally, by solving numerically the dimensionless dispersion equation, the instability domains of the Alfvén waves are obtained. It is shown that there are possible decay processes and modulational instabilities.