Analytical construction and visualization of nonlinear waves in the (2+1) dimensional Kadomtsev-Petviashvili-Sawada-Kotera-Ramani equation with stability analysis

Abstract In this study, we investigate the (2+1)-dimensional Kadomtsev–Petviashvili–Sawada–Kotera–Ramani (KPSKR) equation, a physically significant model describing nonlinear wave phenomena in higher-dimensional spaces. Utilizing the improved modified extended tanh-function method, we derive a diverse spectrum of exact analytical solutions. These include bright solitons, singular solitons, singular periodic waves, and hyperbolic function solutions. The physical characteristics and dynamical behaviors of the obtained solutions are further elucidated through comprehensive two-dimensional and three-dimensional graphical visualizations, offering insight into the complex wave structures governed by the KPSKR equation. The results highlight the versatility of the proposed method and the rich nonlinear dynamics inherent in the model.