Nonlinear wave dynamics in higher dimensions: analytical solutions for the coupled Konno-Oono and Kadomtsev-Petviashvili modified extended wave equations

The paper explores analytical solutions to the coupled Konno-Oono and Kadomtsev-Petviashvili (modified) extended wave (KP-MEW) equations in (2 +1)-dimensions, which have applications in the study of nonlinear wave propagation in shallow water, plasma, and optical systems. The method (Riccati Modified Extended Simple Equation Method) was applied to provide us with a wide range of exact traveling wave solutions as hyperbolic, trigonometric, exponential, and rational. The solutions obtained are highly nonlinear, including soliton pulses, periodic waves, kink-like structures and blow-up modes, which give an understanding of the interaction of waves and their stability. It is important to note that the rational-type solutions are a new category that has never been mentioned in other studies. The authors generalize the previous studies by providing a coherent structure in building different families of solutions, which reveal the usefulness and flexibility of the suggested approach in investigating the nonlinear wave dynamics in higher dimensions.