Novel evolutionary behaviors of localized wave solutions and bilinear auto-Backlund transformations for the generalized (3+1)-dimensional Kadomtsev-Petviashvili equation

Water waves are common phenomena in nature, which have attracted extensive attention of researchers. In the present paper, we first deduce five kinds of bilinear auto-Backlund transformations of the generalized (3+1)-dimensional Kadomtsev-Petviashvili equation starting from the specially exchange identities of the Hirota bilinear operators; then, we construct the N-soliton solutions and several new structures of the localized wave solutions which are studied by using the long wave limit method and the complex conjugate condition technique. In addition, the propagation orbit, velocity and extremum of the first-order lump solution on (x, y)-plane are studied in detail, and seven mixed solutions are summarized. Finally, the dynamical behaviors and physical properties of different localized wave solutions are illustrated and analyzed. It is hoped that the obtained results can provide a feasibility analysis for water wave dynamics.