The nonlinear propagation of electrostatic solitary structures in unmagnetized multispecies plasmas is studied in the wave frame, where they are stationary, via the recently developed McKenzie approach as an alternative to the more usual Sagdeev pseudo-potential method. This way of looking at the problem brings out the gas-dynamic aspects, which then allow a straightforward characterization of the solitary wave possibilities in terms of the species' own sonic points and of the global charge neutral points. A qualitative discussion of ion-, dust- and electron-acoustic solitary waves is given in terms of these concepts and the results are contrasted with those obtained by other methods. Ion-acoustic solitons can be shown to always be compressive, without invoking simplifying assumptions such as cold ions or Boltzmann electrons. Beam-plasmas can also be studied, as in the electron-acoustic solitary wave model for the spiky structures of the broadband electrostatic noise observed in the auroral regions of the Earth's magnetosphere. Such solitons always show a potential dip.