  Discussion is given of non-linear soliton behavior including coupling between
electrostatic and electromagnetic potentials for non-relativistic, weakly
relativistic, and fully relativistic plasmas. For plasma distribution functions
that are independent of the canonical momenta perpendicular to the soliton
spatial structure direction there are, in fact, no soliton behaviors allowed
because transverse currents are zero. Dependence on the transverse canonical
momenta is necessary. When such is the case, it is shown that the presence or
absence of a soliton is intimately connected to the functional form assumed for
the particle distribution functions. Except for simple situations, the coupled
non-linear equations for the electrostatic and electromagnetic potentials would
seem to require numerical solution procedures. Examples are given to illustrate
all of these points for non-relativistic, weakly relativistic, and fully
relativistic plasmas.
