Wronskian and Grammian Solutions for the (2 + 1)-Dimensional Extended Kadomtsev–Petviashvili–Boussinesq, Boussinesq, and Kadomtsev–Petviashvili Equations

This paper studies exact wave solutions of the (2+1)-dimensional extended Kadomtsev–Petviashvili–Boussinesq (eKP–BO), Boussinesq (eBO), and Kadomtsev–Petviashvili (eKP) equations using Wronskian and Grammian methods. The Wronskian approach is used to construct N-soliton solutions, including stable kink-type solitons and resonant Y-type wave structures. By applying the long-wave limit, multi-lump solutions are also obtained, and their trajectories and amplitudes are analyzed. The results show that the soliton and lump waves maintain their localized structures during evolution, while their propagation paths depend on the governing equation. In addition, the Grammian method produces hybrid lump–soliton solutions, revealing a wider variety of nonlinear wave interactions. These results demonstrate the effectiveness of the proposed methods for exploring complex wave dynamics in the considered equations.