Study of small perturbations of a stationary state in a model of upper hybrid plasma oscillations

We show that a constant external magnetic field, generally speaking, is not able to prevent breaking (loss of smoothness) of relativistic plasma oscillations, even if these are arbitrarily small perturbations of the zero steady state. This result sharply differs from the nonrelativistic case, where the breaking of oscillations can be suppressed at any initial deviations by increasing the magnetic field strength. Nevertheless, even in the relativistic case, there are subclasses of solutions corresponding to solutions that are globally smooth in time.