The elastic-fusion-coupled interaction for the Boussinesq equation and new soliton solutions of the KP equation

In this paper, by using of the classical Darboux transformation method, we obtain explicit solutions of the Boussinesq equation and the Kadomtsev-Petviashvili (KP) equation. Especially, for the Boussinesq equation we get explicit solutions describing the elastic-fusion-coupled interaction, which is a new phenomenon for the Boussinesq equation. For the KP equation, we obtain new soliton solutions.