Computational soliton solutions to $$(3+1)$$ ( 3 + 1 ) -dimensional generalised Kadomtsev–Petviashvili and $$(2+1)$$ ( 2 + 1 ) -dimensional Gardner–Kadomtsev–Petviashvili models and their applications

Abstract

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 are of 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 arising in contemporary physics.