A simplified symbolic computation method based on Hirota bilinear equations for constructing multiple-order rogue waves

Abstract

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 For instance, simpler first- to fourth-order rogue waves, as well as fifth-order rogue waves that were previously unpublished, are yielded by the simplified method for a generalized (2+1)-dimensional Kadomtsev-Petviashvili equation. To be honest, the obtained results in this paper substantially improve or complement the corresponding conditions in the references [17,18]. As a consequence,~this paper gives a new idea to derive high-order rogue waves for the generalized (2+1)-dimensional Kadomtsev-Petviashvili equation.