New exact solutions and related dynamic behaviors of a (3+1)-dimensional generalized Kadomtsev–Petviashvili equation

In this paper, a (3+1)-dimensional generalized Kadomtsev–Petviashvili equation is systematically investigated based on the Hirota bilinear method. The explicit N-soliton solution and the bright and dark multi-soliton solutions of it are first derived. Next, various bright and dark higher-order breather solutions, including the periodic line wave solutions, as well as the hybrid solutions composed of solitons, breathers, and periodic line waves, are proposed by virtue of the complex conjugate constraints on the parameters. Then, applying the long wave limit to the N-soliton solution, the bright and dark lump solutions and line rogue wave solutions of the (3+1)-dimensional generalized Kadomtsev–Petviashvili equation are constructed. The semi-rational solutions composed of breathers, lumps, solitons, and line rogue waves are further discussed. These new exact solutions all appear in pairs of bright and dark, which can be interpreted by the uplifts and collapses of energy. In addition, the dynamic behaviors of these exact nonlinear wave solutions are vividly demonstrated by their corresponding three-dimensional diagrams, sectional drawings, and density plots with contours.