A comparative study of the instabilities of two classes of nonlinear waves in cold plasmas

Results are presented of the stability analysis against small parallel perturbations of two classes of nonlinear waves in cold unmagnetized electron plasmas emphasizing similarities and differences. The first class is a stationary longitudinal wave set up by two counter-streaming cold electron beams; the second class is a mixed transverse-longitudinal standing wave in a relativistic plasma with a circularly polarized transverse electric field whose amplitude is periodically modulated in the longitudinal direction. The perturbation dispersion relations are discussed for all perturbation wavenumbers and all nonlinear wave amplitudes. Particular attention is given to the appearance of gaps in those dispersion relations. (author)