Integrability and multiple-rogue wave solutions for the generalized (2+1)-dimensional Kadomtsev-Petviashvili equation: A simplified symbolic computation apporach

The computation of higher-order rogue waves can be a time-consuming process. Hirota bilinear equations with controllable centers for all orders of rogue wave solutions can be solved by a simplified symbolic computation method. Only one-third of the computational effort needed by the original method is required by the simplified one, for very high orders. For instance, simpler first- to fourth-order rogue waves, as well as fifth-order rogue waves that were previously unpublished, are yielded by the simplified method for a generalized (2+1)-dimensional Kadomtsev-Petviashvili equation. Moreover, the structural characteristics of the roots of auxiliary polynomials associated with higher-order rogue waves were systematically examined within the complex plane. In addition, a comprehensive analysis was conducted on their dynamic behavior by tracking the temporal evolution of the rogue wave profiles at the same time. To be honest, the obtained results in this paper substantially improve or complement the corresponding conditions in the known references. As a consequence, this paper gives a new idea to derive high-order rogue waves for the generalized (2+1)-dimensional Kadomtsev-Petviashvili equation.