We provide a brief description of three examples of nonlinear stationary waves, chosen because they exhibit interesting and unusual properties. The first is the classical ion‐acoustic soliton which, by a suitable admixture of negative heavy ions, can exhibit a rarefractive structure associated with a potential dip. The second is the whistler “oscilliton” which possesses the classical soliton pulse, superimposed on which are fine scale oscillations in the longitudinal and transverse flow speeds. This wave arises from the balance between the sum of the Reynolds stresses of the electrons and protons and the magnetic Maxwell stresses. The inclusion of negatively charged heavy ions also ensures that the left handed proton cyclotron mode may exhibit this type of intricate structure. Finally we discuss the electrostatic‐ion‐cyclotron mode which can possess both soliton (for subsonic speeds) and oscillatory (for supersonic speeds) solutions. In the latter case spiky wave forms can be constructed by a drive towards the sonic point in the compressive phase of the wave. © 2004 American Institute of Physics