Real and complex multi solitons, soliton molecules, asymmetric solitons and diverse wave solutions to the (2+1)-dimensional Sawada–Kotera–Kadomtsev Petviashvili equation

This work explores some exact solutions to the (2[Formula: see text]1)-dimensional Sawada–Kotera–Kadomtsev Petviashvili equation (SKKPe) for the fluid mechanic. First, by taking advantage of the Hirota method, the real and complex multi-soliton solutions (MSSs) are derived. Then, the soliton molecules (SMs) are extracted via taking the velocity resonance condition (VRC) to the real MSSs and the asymmetric solitons (ASs) are developed by selecting the appropriate parameters. In the end, the abundant wave solutions are investigated by utilizing the sub-equation method (SEM). The wave structures of the attained solutions are displayed graphically to unveil the nonlinear physical characteristics. The obtained solutions in this work allow us to investigate the nonlinear dynamics of the (2[Formula: see text]1)-dimensional SKKPe better.