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

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 Backlund 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 (u) over cap is butterfly shaped.

Automated summary

The paper studies a multicomponent weakly interacted generalized Kadomtsev-Petviashvili equation, deriving various types of equations by choosing different coefficients, and deducing its Backlund transformation and Hirota bilinear equations. By focusing on the two-component case, soliton and rogue wave solutions were solved in detail, with the rogue wave solutions showing distinct eye and butterfly shapes for the first and second components respectively.