Long wavelength, nonlinear perturbations of the Brillouin flow equilibrium on magnetically insulated lines

The present investigation shows that in the limit of long but finite wavelengths and small but nonvanishing amplitudes, TM perturbations traveling along the direction of electron flow in magnetically insulated lines are governed by a Korteweg-deVries' equation. This equation agrees with earlier results derived independently in the appropriate limits of either infinitely long wavelengths or vanishingly small amplitudes. Either periodic or soliton solutions to the governing equation can exist. In particular, the solitons consist physically of a bump or depression in the number density of sheath electrons which propagates along the line.