On the multicomponent weakly interacted generalized (3 + 1)‐dimensional Kadomtsev–Petviashvili equation

Abstract

In this paper, we study a multicomponent weakly interacted generalized (3 + 1)‐dimensional Kadomtsev–Petviashvili equation (MWIGKP) from which we can get many different types of equations by choosing different coefficients. Then, we deduce the Bäcklund transformation and Hirota bilinear equations of the equation. Finally, taking the two‐component case as an example, we solve the soliton solutions and the rogue wave solutions in detail. By considering the figures of the weakly coupled rogue wave solutions, we can see that the figure corresponding to first component u is eye shaped, while the figure corresponding to the second component is butterfly shaped.