Rational solutions and rogue waves of the generalized (2+1)-dimensional Kadomtsev–Petviashvili equation

Abstract

There is fundamental and applicative interest in finding rogue wave solutions that “appears from nowhere and disappears without a trace”. Here, we analytically derived multi-order rogue wave solutions for a generalized (2+1)-dimensional Kadomtsev–Petviashvili (KP) equation through its bilinear form and symbolic computation. These solutions comprise four independent solutions of the bilinear equation and depend on two arbitrary parameters, which can be used to shape the appearance of the wave. Moreover, we have looked into the inner mechanism between the polynomial Fn and the rogue wave solution un.