In part 1 (Infeld 1972), it was shown that a nonlinear stationary wave in a cold plasma is marginally stable to all perturbations that are functions of the spatial direction parallel to the direction of propagation only. The stability analysis is extended here in part 2 to include general spatial variations. Within the limitations of the treatment, it is found that, for wave amplitudes up to maximal value (onset of trapping), the wave is marginally stable. Hence one would expect these large-amplitude cold plasma waves to exist in practice.
The one-dimensional analysis of part 1 is also extended to include waves with relativistic velocities, and such waves are again found to be marginally stable.