Multiple-order rogue waves for the generalized (2+1)-dimensional Kadomtsev–Petviashvili equation

Abstract Starting with the bilinear form of the generalized ( 2 + 1 )-dimensional Kadomtsev–Petviashvili equation, multiple-order rogue waves have been obtained through symbolic computation. Maximum and minimum values as well as their trajectories for the first order rogue wave are systematically discussed. Moreover, the second order and third order rogue waves are established by eliminating the impact of the mixed partial derivative, and the numerical simulations are demonstrated to visualise their temporal evolution.