In this paper, we use the generalised Hirota bilinear method (GHBM). With the help of symbolic calculations and applying the used method, we solve the Kadomtsev–Petviashvili (KP)-like equation with $p$ = 3 to obtain some new lump, periodic kink-wave and solitary wave solutions. All solutions have been verified with their corresponding equations with the aid of the Maple package program.
