Abstract
In this paper, a generalised $$(3+1)$$ -dimensional Kadomtsev–Petviashvili (KP) equation is considered. By transforming it into the bilinear form, one-, two- and multisoliton solutions are obtained. What is more, the Wronskian and Grammian solutions are also presented according to the Plucker relation and the Jacobi identity for determinants. In order to have an in-depth understanding of the dynamical properties of the equation, examples of each solution are given and some of them are plotted.
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