The dynamics of some exact solutions of the (3+1)-dimensional generalized shallow water wave equation

The (3+1)-dimensional generalized shallow water wave equation is systematically investigated in this paper based on the Hirota bilinear method. The N-soliton solution and the higher-order kink-shaped breather solutions of the (3+1)-dimensional generalized shallow water wave equation are first proposed. Then, the line rogue wave solution and various hybrid solutions consisting of the breather, the kink-shaped soliton and the periodic solutions are discussed. Furthermore, the lump solutions of it are derived by using the long wave limit of the N-soliton solution. In addition, the diverse semi-rational solutions composed of lumps, kink solitons, line rogue wave and breathers enrich the research contents of the (3+1)-dimensional generalized shallow water wave equation. The dynamic behaviors of these exact solutions are vividly presented by their respective three-dimensional diagrams and density plots with contours.