Nonlinear characteristics of various local waves on nonzero backgrounds of a (2+1)-dimensional generalized Kadomtsev–Petviashvili equation with variable coefficients

In this paper, a (2+1)-dimensional generalized Kadomtsev–Petviashvili (KP) equation with variable coefficients is studied by the symmetry transformation and bilinear neural network method. By constructing the “3-3-1” neural network models, various important analytical solutions of the equation are successfully obtained, including the breather wave solutions, rogue wave solutions and interaction solutions. Then the evolution behaviors of these analytical solutions are analyzed through selecting appropriate parameters and 3D animations. Specially, three interesting interaction phenomena are presented, i.e., the rogue waves are generated from two moving solitary waves, which have different evolution behaviors on different nonzero background waves. The study of various local waves is helpful to understand the dynamic characteristics of the nonlinear waves, and may be further applied in the fields of scientific research and engineering practice. This paper is used to provide the theoretical guidance and references for the research of studying the evolutions of nonlinear waves in optics, fluid mechanics, and other fields.