Rogue wave solutions of (3+1)-dimensional Kadomtsev-Petviashvili equation by a direct limit method

On the bases of N-soliton solutions of Hirota's bilinear method, high-order rogue wave solutions can be derived by a direct limit method. In this paper, a (3+1)-dimensional Kadomtsev-Petviashvili equation is taken to illustrate the process of obtaining rogue waves, that is, based on the long-wave limit method, rogue wave solutions are generated by reconstructing the phase parameters of N-solitons. Besides the fundamental pattern of rogue waves, the triangle or pentagon patterns are also obtained. Moreover, the different patterns of these solutions are determined by newly introduced parameters. In the end, the general form of N-order rogue wave solutions are proposed.