Such structures arise due to a detailed balance between nonlinearity and dispersion. A Plasma, being a nonlinear medium, tends to steepen waves by the coupling of larger to smaller scales. As a result of these two competing mechanisms, stable structures can arise. It is precisely this detailed balance between nonlinearity and dispersion that gives solitons and double layers their stability. However, any wave branch with the desired dispersive characteristics can lead to solitary waves.
Double layers are potential steps.
They are sometimes called electrostatic shocks. They differ from solitons in that their asymmetric potential profile indicates a peak in the electric field that can accelerate particles to high energies. It is thought that double layers play a role in accelerating particles in the auroral regions.