Waves launched into a magnetized plasma, when it is rapidly compressed were studied in the late 1950s by Adlam and Allen. In this paper we show that the equations describing large amplitude magnetized plasma waves, or Adlam-Allen waves, can be reduced to a, single nonlinear equation, namely the Korteweg-de Vries equation and that the solutions of this equation are in agreement with the results obtained previously by Adlam and Allen. The solutions of both the Adlam-Allen equations and the Korteweg-de Aries equation take the form of solitary waves; and periodic wave trains.
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