NONLINEAR CONDUCTIVITY AND MAGNETOPLASMA WAVES IN COMPENSATED METALS AND SEMI-METALS

The existence of non-linear magnetoplasma waves in compensated metals and semimetals in the presence of a strong magnetic field is predicted . Non-linearity in the case considered is caused by the influence of t he magnetic field of the wave on the dynamics of the electrons and hol es. The conductivity tensor is calculated neglecting the spatial dispe rsion and is shown to be in the non-linear regime a differential-with respect to time-operator which is a manifestation of the temporal disp ersion effects. The shape of the wave solution obtained is determined by two parameters: the amplitude H and the phase velocity V. When the amplitude is small and V < V-A, where V-A is the Alfven velocity, the solution transforms into the well-known linear magnetoplasma wave. It is shown that, contrary to the linear case, the non-linear magnetoplas ma wave exists when the phase velocity is both less and larger than V- A. It is established that with increase of the velocity and the amplit ude being fixed the quasiharmonic wave turns into a series of pulses, the interval between which is growing infinitely. In the aperiodic lim it the wave becomes a one-parameter soliton. Its velocity is larger th an V-A and depends linearly on H. With increase of H, when V is fixed, the period of the magnetoplasma wave descends and the wave shape beco mes a series of sharp spikes. Thus, when V < V-A we have transition fr om a linear wave to an anharmonic one, while when V > V-A We have a tr ansition from a soliton to a sequence of pulses. Both the soliton and the non-linear periodic wave with V > V-A have no analogues in the lin ear case. These electromagnetic waves are essentially non-linear even at small-in comparison with the external magnetic field-amplitudes.