Multiple-soliton solutions for the Lax–Kadomtsev–Petviashvili (Lax–KP) equation

A new completely integrable dispersive equation is derived. The new equation is obtained by extending the Lax fifth-order equation using the sense of the Kadomtsev–Petviashvili (KP) equation in extending the KdV equation. The newly derived Lax–Kadomtsev–Petviashvili (Lax–KP) equation is investigated by using the tanh–coth method and the Hirota bilinear method to derive single soliton solution and N-soliton solutions, respectively. The study highlights the multiple-soliton solutions of the derived completely integrable equation.