Plasmas can support a rich variety of waves. Many satellite-based experiments show evidence of waves in space. Sometimes these are large amplitude solitary waves.
Space plasmas are often not in thermodynamic equilibrium, and examples such as two-temperature plasmas, and non-Maxwellian velocity distributions (with a superthermal "tail"), are commonly observed. The latter are well modelled by a kappa distribution.
We first give an outline of some of the waves that can play an important role in typical multi-component space plasmas. We shall then discuss some effects of high-energy tails on wave behaviour, with an application to Saturn's magnetosphere. Finally we will discuss existence domains and some characteristics of acoustic solitons in multi-species space plasmas.