Dynamics of real and complex multi-soliton solutions, novel soliton molecules, asymmetric solitons and diverse wave solutions to the Kadomtsev-Petviashvili equation

The main center of this exploration is to extract some exact solutions of the (2+1)-dimensional Kadomtsev-Petviashvili equation (KPe), which can be used to model the long wave water waves with weak nonlinear restoring forces and frequency dispersion. First, the Hirota method is exerted to develop the real and complex multi-soliton solutions. Then, the soliton molecules (SMs) are derived by introducing the velocity resonance (VR). In addition, the asymmetric solitons (ASs) are also found through adjusting the initial phase values. Eventually, two efficacious methods, Wang’s direct mapping method-II (WDMM-II) and the variational method (VM), are employed to explore the other abundant wave solutions, including the bright soliton, dark soliton, periodic wave and the singular wave solutions. The profiles of the acquired exact solutions are depicted to exhibit the corresponding physical attributes. The findings of this research can enable us master the dynamics of the considered KPe better.