Exact Soliton Structures and Modulation Instability in Extended Kadomtsev–Petviashvili–Boussinesq Equation

In this study, we consider an extended form of the Kadomtsev–Petviashvili–Boussinesq equation motivated by wave propagation phenomena in dissipative media. The primary aim of this work is to construct exact analytical solutions and clarify the types of nonlinear wave structure admitted by the considered model. For this purpose, the Riccati equation expansion method is applied for the first time within this framework. This method allows us to obtain several distinct families of solitary wave solutions whose qualitative behaviors and physical characteristics are illustrated through graphical representations. In addition, modulation instability analysis is carried out to assess the stability of continuous wave solutions and further elucidate the underlying nonlinear dynamics of the system.