General high-order localized waves and interaction solutions to the new (3+1)-dimensional shallow water wave equation in Engineering and Physics

A systematic investigation of the (3+1)-dimensional extended shallow water wave (3D-eSWW) equation is carried out using the Hirota bilinear method. The N-soliton and higher-order breather solutions for the 3D-eSWW equation are first proposed. Subsequently, 2 kinds of breather-soliton hybrid solutions are discussed. Furthermore, M-lump and line rogue wave solutions of the 3D-eSWW equation are derived. In addition, lump, soliton, and breather solutions, referred to as varied semi-rational solutions, significantly enhance the 3D-eSWW equation’s research scope. More importantly, we delve into the intriguing realm of physical collisions among interacting nonlinear waves. Through the intuitive presentation of 3-dimensional graphics and numerical simulations, the characteristics of these hybrid solutions are more clearly revealed.