The aim of this paper is to investigate a class of generalised Kadomtsev–Petviashvili (KP) and B-type Kadomtsev–Petviashvili (BKP) equations, which include many important nonlinear evolution equations as its special cases.By applying the fundamental Pfaffian identity, a general Pfaffian formulation is established and all the involved generating functions for Pfaffian entries need to satisfy a system of combined linear partial differential equations. The illustrative examples of the presented Pfaffian solutions are given for the (3+1)-dimensional generalised KP, Jimbo–Miwa and BKP equations. Moreover, we use the linear superposition principle to generate exponential travelling wave solutions and mixed resonant solutions of the considered equations.

This paper aims to explore a kind of lump solutions in nonlinear dispersive waves with higher-order rational dispersion relations.We show that the second member in the commuting Kadomtsev–Petviashvili hierarchy is such an example, and construct its lump solutions, based on a Hirota trilinear form. The presented lump solutions have one peak and two valleys, where the global maximum and minimum values are achieved. A few three dimensional plots and contour plots are made for a specific example of the lumps.