In this paper, the auxiliary equation method is successfully applied to compute analytical solutions for (3+1)-dimensional generalised Kadomtsev–Petviashvili and (2+1)-dimensional Gardner–Kadomtsev–Petviashvili equations, by introducing simple transformations. These results hold numerous travelling wave solutions that areof key importance which provide a powerful mathematical tool for solving nonlinear wave equations in recent era of applied science and engineering. The method can also be extended to other nonlinear evolution models arisingin contemporary physics.
