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Nonlinear acoustic waves in partially ionized collisional plasmas

Nonlinear propagation of acoustic-type waves in a partially ionized three-component collisional plasma consisting of electrons, ions and neutral particles is investigated. For bidirectional propagation, we show that the small- but finite-amplitude waves are governed by the Boussinesq equation, which for unidirectional propagation near the acoustic speed reduces to the usual Korteweg de Vries equation. For large-amplitude waves, we demonstrate that the relevant fluid equations are integrable in a stationary frame, and we explicitly obtain the parameter values for the existence of finite-amplitude solutions. In both cases, we take into account the different temperatures of the individual species. The relevance of the results to the earth's ionospheric plasma in the lower altitude ranges is pointed out.