Multiple-soliton solutions for the KP equation by Hirota’s bilinear method and by the tanh–coth method

In this work we use the Hirota’s direct method combined with the simplified version of this method to determine the N-soliton solutions, N = 1, 2, 3, 4, 5 for the Kadomtsev–Petviashvili (KP) equation. The one-soliton solutions will be handled by the tanh–coth method. The work emphasizes the power of the two methods that will be used.