W-shape and abundant of other solitary wave solutions of the positive Gardner Kadomtsov–Petviashivilli dynamical model with applications

In this study, we explore the positive Gardner Kadomtsov–Petviashivilli (KP) equation using the Generalized Ricatti Equation Mapping Method (GREMM). The KP equation describes the behavior of quasi-one dimensional shallow-water waves in the absence of surface tension and viscosity effects. By employing GREMM, we derive analytical solutions expressed in terms of hyperbolic, rational trigonometric, and exponential functions. These solutions are original and have not been previously documented. They have significant applications in engineering and other applied sciences. By assigning suitable values to the parameters of specific solutions, we generate new graphical structures that enhance our understanding of the physical phenomenon described by this model. The computational effort and resulting outputs demonstrate the effectiveness and power of the proposed technique, which can be extended to other nonlinear models in mathematical physics and various scientific disciplines.