It is shown that the Kadomtsev-Petviashvili equation can be reduced first to the Boussinesq or Korteweg-de Vries equation, and secondly to the first or second Painlevé equation by means of infinitesimal transformations of Lie's method. The soliton solutions moving in non-steady and non-uniform background are also obtained.
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Tajiri et al. (1982) studied this question.
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