LAUSR

In this work, the generalized $$(3+1)$$ -dimensional variable coefficients Kadomtsev–Petviashvili equation, widely used in fluids or plasmas, is analyzed via the unified method and its general form. The multi-soliton rational solutions are obtained including single- and double-soliton rational solutions. Single-soliton shaping and the interactions of double-soliton are graphically discussed in different choices of coefficients. Single-soliton wave keeps its shape, velocity and amplitude unchanged and propagates periodically in a certain direction. The double-soliton waves do not change in shapes, velocities and amplitudes before and after the collisions. We conclude that collisions between the double-soliton waves are elastic and they are not affected by the coefficients of the equation.