Parallel propagating electromagnetic solitons and oscillitons in space plasmas and in relativistic electron-positron plasmas

An overview is given of methods to study weak and strong nonlinear modes in multispecies plasmas, with a discussion of how they correspond (or not) for phenomena at not too strong amplitudes. Reductive perturbation analysis leads for weak nonlinear waves to several well known nonlinear evolution equations. In contrast, strong nonlinear phenomena are dealt with by immediately looking for stationary solutions of the model equations. While this works well for electrostatic modes via the Sagdeev pseudopotential technique, large amplitude, parallel propagating solitary electromagnetic waves occur as oscillitons, for which the correct nonlinear evolution equation is still lacking. Electromagnetic modes in (relativistic) electron-positron plasmas are an exception, in that they give pure solitons, both at large and smaller nonlinear amplitudes. The behaviour of the wave magnetic field is expressed through an energy integral that involves the Mach number of the structure, thus yielding the limits on the allowable Mach numbers and soliton amplitudes.